Jacques H.H. Perk's Vita Page

BIRTH DATE: November 4, 1948
CITIZENSHIP: Netherlands, Permanent Resident USA
ORCID ID: 0000-0002-7503-1640

EDUCATION:

Qualifier in Theoretical Physics, University of Amsterdam, 1971
“M.Sc.” Report: The Theorem of Marcinkiewicz (in Dutch)

Drs. in Theoretical Physics, University of Amsterdam, 1974
Thesis: Bethe Ansatz and One-Dimensional Quantum Systems (in Dutch)

Dr. of Mathematics and Physical Sciences, University of Leiden, 1979
Thesis: Time-Dependent Correlations in the One-Dimensional XY-Model

PROFESSIONAL EXPERIENCE:

Professor of Physics, Department of Physics, OSU, July 1991 - continuing
Invited Professor RIMS, Kyoto, May 1991 - June 1992
Associate Professor, Department of Physics, OSU, August 1988 - July 1991
Assistant Professor, ITP, SUNY, Stony Brook, NY, September 1981 - August 1988
Postdoctoral Fellow, ITP, SUNY, Stony Brook, NY, September 1979 - August 1981
Research Fellow, Instituut-Lorentz, Leiden1975--1979

Ph.D. Theses under supervision of J.H.H. Perk:

Lee-Fen Ko, Correlation Functions of the Ising Model and the Eight-Vertex Model, Stony Brook, August 1985.
M. Tobias Haas, Q-State Generalizations of the Hard Hexagon Model, Stony Brook, June 1987.
Xiang-Peng Kong, Wave-Vector Dependent Susceptibility of the Two-Dimensional Ising Model, Stony Brook, September 1987.
Bai-Qi Jin, Some Aspects of the Chiral Potts Model and the Ising Model, Stillwater, Oklahoma, August 2001.

Publications of Jacques H.H. Perk (omitting abstracts):

Th.J. Siskens, H.W. Capel, and J.H.H. Perk, Antiferromagnetic chain with alternating interactions and magnetic moments, Phys. Lett. A 53 (1975) 21-22.
J.H.H. Perk, H.W. Capel, M.J. Zuilhof, and Th.J. Siskens, On a soluble model of an antiferromagnetic chain with alternating interactions and magnetic moments, Physica A 81 (1975) 319-348.
J.H.H. Perk and H.W. Capel, Antisymmetric exchange, canting and spiral structure, Phys. Lett. A 58 (1976) 115-117.
L.W.J. den Ouden, H.W. Capel, J.H.H. Perk, and P.A.J. Tindemans, Systems with separable many-particle interactions I, Physica A 85 (1976) 51-70.
L.W.J. den Ouden, H.W. Capel, and J.H.H. Perk, Systems with separable many-particle interactions II, Physica A 85 (1976) 425-456.
H.W. Capel and J.H.H. Perk, Autocorrelation function of the x-component of the magnetization in the one-dimensional XY-model, Physica A 87 (1977) 211-242.
J.H.H. Perk and H.W. Capel, Time-dependent xx-correlations in the one-dimensional XY-model, Physica A 89 (1977) 265-303.
J.H.H. Perk, H.W. Capel, and Th.J. Siskens, Time-correlation functions and ergodic properties in the alternating XY-chain, Physica A 89 (1977) 304-325.
J.H.H. Perk, H.W. Capel, and L.W.J. den Ouden, Convex-envelope formulation for many-particle separable interaction, Physica A 89 (1977) 555-568.
J.H.H. Perk and H.W. Capel, Gouden doctoraat, [Golden Doctorate, 50th anniversary of Ph.D. theses of G.E. Uhlenbeck and S.A. Goudsmit, in Dutch], Nederlands Tijdschrift voor Natuurkunde B43(17) (1977) 99-100.
H.W. Capel and J.H.H. Perk, Transverse correlations in the one-dimensional XY-model, Ann. Israel Phys. Soc. 2 (1978) 586-589.
J.H.H. Perk and H.W. Capel, Convex-envelope formulation for separable interactions, Ann. Israel Phys. Soc. 2 (1978) 1027-1030.
J.H.H. Perk and H.W. Capel, Transverse correlations in the inhomogeneous XY-model at infinite temperature, Physica A 92 (1978) 163-184.
H.W. Capel, J.H.H. Perk, and L.W.J. den Ouden, Critical-exponent renormalization and first-order transitions, Phys. Lett. A 66 (1978) 437-439.
H.W. Capel, L.W.J. den Ouden, and J.H.H. Perk, Stability of critical behaviour, critical-exponent renormalization and first-order transitions, Physica A 95 (1979) 371-416.
J.H.H. Perk and H.W. Capel, Time-dependent correlation functions in the high-temperature limit for the XY-chain and the Ising-chain in a transverse magnetic field, J. Appl. Phys. 50 (1979) 1771-1772.
J.P. Groen, H.W. Capel, J.H.H. Perk, T.O. Klaassen, and N.J. Poulis, Spin dynamics of an S=1/2 antiferromagnetic Heisenberg chain at low temperatures, Physica B 97 (1979) 126-144.
J.H.H. Perk and H.W. Capel, Time- and frequency-dependent correlation functions for the homogeneous and alternating XY-models, Physica A 100 (1980) 1-23.
J.P. Groen, H.W. Capel, J.H.H. Perk, T.O. Klaassen, and N.J. Poulis, Proton relaxation in an S=1/2 antiferromagnetic linear chain system, J. Magn. Magn. Mat. 15-18 (1980) 684-686.
B.M. McCoy and J.H.H. Perk, Two-spin correlation functions of an Ising model with continuous exponents, Phys. Rev. Lett. 44 (1980) 840-844.
J.H.H. Perk and Z. Popowicz, Comment on ‘New Exact Solutions of the Classical Sine-Gordon Equation in 2+1 and 3+1 Dimensions’, Phys. Rev. D 23 (1981) 2482-2483.
J.H.H. Perk, Equations of motion for the transverse correlations of the one-dimensional XY-model at finite temperature, Phys. Lett. 79A (1980) 1-2.
J.H.H. Perk, Quadratic identities for Ising model correlations, Phys.Lett. 79A (1980) 3-5.
J.H.H. Perk, Nonlinear partial difference equations for Ising model n-point Green's functions, Proc. II International Symposium on Selected Topics in Statistical Mechanics, Dubna, August 25-29, 1981, (JINR, Dubna, USSR, 1981), pp. 138-151. A scanned PDF file is available.
J.H.H. Perk and C.L. Schultz, New families of commuting transfer matrices in q-state vertex models, Phys. Lett. 84A (1981) 407-410.
B.M. McCoy and J.H.H. Perk, Continuous exponents of spin correlation functions of inhomogeneous layered Ising models, Lecture Notes in Mathematics, Vol. 925, (Springer, Berlin, 1982), pp. 12-27.
L.W.J. den Ouden, H.W. Capel, and J.H.H. Perk, Critical-exponent renormalization, first-order transitions, and demagnetizing effects for Schofield’s linear model, Physica A 105 (1981) 53-85.
B.M. McCoy, J.H.H. Perk, and T.T. Wu, Ising field theory: quadratic difference equations for the n-point Green’s functions on the square lattice, Phys. Rev. Lett. 46 (1981) 757-760.
J.H.H. Perk and C.L. Schultz, Families of commuting transfer matrices in q-state vertex models, in Non-linear integrable systems – classical theory and quantum theory, Proceedings of RIMS Symposium organized by M. Sato, Kyoto, Japan, 13-16 May 1981, eds. M. Jimbo and T. Miwa, (World Scientific, Singapore, 1983), pp. 135-152.
C.A.M. Mulder, H.W. Capel, and J.H.H. Perk, The Heisenberg model: Classical ground state and bilinear spin-wave theory, Physica B 112 (1982) 147-187.
J.H.H. Perk and C.L. Schultz, Diagonalization of the transfer matrix of a nonintersecting string model, Physica A 122 (1983) 50-70.
B.M. McCoy, J.H.H. Perk, and R.E. Shrock, Time-dependent correlation functions of the transverse Ising chain at the critical magnetic field, Nucl. Phys. B 220 [FS8] (1983) 35-47.
B.M. McCoy, J.H.H. Perk, and R.E. Shrock, Correlation functions of the transverse Ising chain at the critical field for large temporal and spatial separations, Nucl. Phys. B 220 [FS8] (1983) 269-282.
H. Au-Yang and J.H.H. Perk, Ising correlations at the critical temperature, Phys. Lett. A 104 (1984) 131-134.
J.H.H. Perk and H. Au-Yang, Ising models and soliton equations, Proc. III International Symposium on Selected Topics in Statistical Mechanics, Dubna, August 22-26, 1984, (JINR, Dubna, USSR, 1985), Vol. II, pp. 138-151. A scanned PDF file is available.
J.H.H. Perk, H.W. Capel, G.R.W. Quispel, and F.W. Nijhoff, Finite-temperature correlations for the Ising chain in a transverse field, Physica 123A (1984) 1-49.
L.-F. Ko, H. Au-Yang, and J.H.H. Perk, Energy-density correlation functions in the two-dimensional Ising model with a line defect, Phys. Rev. Lett. 54 (1985) 1091-1094.
H. Au-Yang and J.H.H. Perk, Toda lattice equation and Wronskians in the 2d Ising model, Physica D 18 (1986) 365-366.
H. Au-Yang, T.M. Haas, L.-F. Ko, and J.H.H. Perk, Some new results on exactly solvable models, Physica D 18 (1986) 386-387.
J.H.H. Perk and F.Y. Wu, Nonintersecting string model and graphical approach: equivalence with a Potts model, J. Stat. Phys. 42 (1986) 727-742.
J.M.R. Roldan, B.M. McCoy, and J.H.H. Perk, Dynamic spin correlation functions of the XYZ chain at infinite temperature: a study based on moments, Physica A 136 (1986) 255-302.
J.H.H. Perk and F.Y. Wu, Graphical approach to the nonintersecting string model: star-triangle equation, inversion relation, and exact solution, Physica A 138 (1986) 100-124.
X.-P. Kong, H. Au-Yang, and J.H.H. Perk, New results for the susceptibility of the two-dimensional Ising model at criticality, Phys. Lett. A 116 (1986) 54-56.
X.-P. Kong, H. Au-Yang, and J.H.H. Perk, Logarithmic singularities of Q-dependent susceptibility of 2-d Ising model, Phys. Lett. A 118 (1986) 336-340.
H. Au-Yang and J.H.H. Perk, Critical correlations in a Z-invariant inhomogeneous Ising model, Physica 144A (1987) 44-104.
X.-P. Kong, H. Au-Yang, and J.H.H. Perk, Comment on a paper by Yamada and Suzuki, Progr. Theor. Phys. 77 (1987) 514-516.
B.M. McCoy and J.H.H. Perk, Relation of conformal field theory and deformation theory for the Ising model, Nucl. Phys. B 285 [FS19] (1987) 279-294.
H. Au-Yang, B.M. McCoy, J.H.H. Perk, S. Tang, and M.-L. Yan, Commuting transfer matrices in the chiral Potts models: Solutions of the star-triangle equations with genus greater than 1, Phys. Lett. 123A (1987) 219-223.
B.M. McCoy, J.H.H. Perk, S. Tang, and C.-H. Sah, Commuting transfer matrices for the four-state self-dual chiral Potts model with a genus-three uniformizing Fermat curve, Phys. Lett. A 125 (1987) 9-14.
H. Au-Yang, B.M. McCoy, J.H.H. Perk, and S. Tang, Solvable models in statistical mechanics and Riemann surfaces of genus greater than one, in Algebraic Analysis, Vol. 1, M. Kashiwara and T. Kawai, eds., (Academic Press, San Diego, 1988), pp. 29-40.
J.H.H. Perk, Star-triangle equations, quantum Lax pairs, and higher genus curves, in Proc. 1987 Summer Research Institute on Theta Functions, Proc. Symp. Pure Math., Vol. 49, part 1, (Am. Math. Soc., Providence, R.I., 1989), pp. 341-354.
H. Au-Yang and J.H.H. Perk, Solution of Hirota’s discrete-time Toda lattice equation and the critical correlations in the Z-invariant Ising model, in Proc. 1987 Summer Research Institute on Theta Functions, Proc. Symp. Pure Math., Vol. 49, part 1, (Am. Math. Soc., Providence, R.I., 1989), pp. 287-293.
R.J. Baxter, J.H.H. Perk, and H. Au-Yang, New solutions of the star-triangle relations for the chiral Potts model, Phys. Lett. 128A (1988) 138-142.
G. Albertini, B.M. McCoy, J.H.H. Perk, and S. Tang, Excitation spectrum and order parameter for the integrable N-state chiral Potts model, Nucl. Phys. B 314 (1989) 741-763.
G. Albertini, B.M. McCoy, and J.H.H. Perk, Commensurate-incommensurate transition in the ground state of the superintegrable chiral Potts model, Phys. Lett. A 135 (1989) 159-166.
G. Albertini, B.M. McCoy, and J.H.H. Perk, Eigenvalue spectrum of the superintegrable chiral Potts model, Proc. Taniguchi Symposium, Kyoto, 1988, in Advanced Studies in Pure Mathematics, Vol. 19, (Kinokuniya-Academic, Tokyo, 1989), pp. 1-55.
H. Au-Yang and J.H.H. Perk, Onsager's star-triangle equation: Master key to integrability, Proc. Taniguchi Symposium, Kyoto, October 1988, in: Advanced Studies in Pure Mathematics, Vol. 19, (Kinokuniya-Academic, Tokyo, 1989), pp. 57-94. See also its preprint.
G. Albertini, B.M. McCoy, and J.H.H. Perk, Level crossing transitions and the massless phases of the superintegrable chiral Potts chain, Phys. Lett. A 139 (1989) 204-212.
H. Itoyama, B.M. McCoy, and J.H.H. Perk, Level crossing, spontaneous parity violation, high T_c superconductivity mechanisms and the chiral Potts chain, Intern. J. Modern Phys. B 4 (1990) 995-1001.
R.J. Baxter, V.V. Bazhanov, and J.H.H. Perk, Functional relations for transfer matrices of the chiral Potts model, Intern. J. Modern Phys. B 4 (1990) 803-870.
J.H.H. Perk, F.Y. Wu, and X.N. Wu, Algebraic Invariants of the O(2) Gauge Transformation, J. Phys. A: Math. Gen. 23 (1990) L131-L135.
W.S. McCullough, J.H.H. Perk, and H.L. Scott, Analysis of a model for the ripple phase of lipid bilayers, J. Chem. Phys. 93 (1990) 6070-6080.
H. Au-Yang and J.H.H. Perk, Star-triangle equations and multicomponent chiral Potts models, Physica A 177 (1991) 139-145.
H. Au-Yang and J.H.H. Perk, Multicomponent chiral Potts models, Intern. J. Mod. Phys. A, Vol. 7, Suppl. 1B (1992) 1007-1023.
H. Au-Yang and J.H.H. Perk, Solutions of the star-triangle equations in (N_α,N_β) Potts models, Intern. J. Mod. Phys. A, Vol. 7, Suppl. 1B (1992) 1025-1046.
H. Au-Yang and J.H.H. Perk, The N→∞ limit of the chiral Potts model, in Proceedings of XXI Differential Geometric Methods in Theoretical Physics, Intern. J. Mod. Phys. A (Proc. Suppl.) 3A (1993) 430-434. See also arXiv:hep-th/9305171.
H. Au-Yang and J.H.H. Perk, The chiral Potts models revisited, J. Stat. Phys. 78 (1995) 17-78. See also its arXiv preprint cond-mat/9407106.
H. Au-Yang and J.H.H. Perk, Chiral Potts model: Exact results and and implications, STATPHYS 19, (World Scientific, Singapore, 1996), pp. 421-428, [invited talk at STATPHYS 19 (Xiamen, China, August 1995)].
H. Au-Yang and J.H.H. Perk, The generalized chiral clock model and its phase diagram, in Statistical Models, Yang-Baxter Equation and Related Topics and Symmetry, Statistical Mechanical Models and Applications, eds. M.L. Ge and F.Y. Wu, (World Scientific, Singapore, 1996), pp. 20-30, [invited talk at STATPHYS 19 Satellite (Nankai, China, August 1995)].
F.W. Nijhoff, J.H.H. Perk, and G.R.W. Quispel, Statistical mechanics, soliton theory, and nonlinear dynamics, Physica A 228 (1996) R13-R22, [Preface, Festschrift in honor of Prof. dr. H.W. Capel on the occasion of his 60th birthday].
H. Au-Yang and J.H.H. Perk, Phase diagram in the generalized chiral clock models, Physica A 228 (1996) 78-101, (in Festschrift in honor of 60th birthday of Prof. dr. H.W. Capel, edited by F.W. Nijhoff, J.H.H. Perk, and G.R.W. Quispel).
H. Au-Yang and J.H.H. Perk, The many faces of the chiral Potts model, Intern. J. Modern Phys. B 11 (1997) 11-26. See also its arXiv preprint q-alg/9609003.
H. Au-Yang and J.H.H. Perk, The large N limits of the chiral Potts model, Physica A 268 (1999) 175-206. See also its arXiv preprint math.QA/9906029.
W.P. Orrick, B. Nickel, A.J. Guttmann, and J.H.H. Perk, The susceptibility of the square lattice Ising model: New developments, J. Stat. Phys. 102 (2001) 795-841. See also its arXiv preprint cond-mat/0103074 and Guttmann's homepage for the series coefficients or its preprint in PDF format.
W.P. Orrick, B. Nickel, A.J. Guttmann, and J.H.H. Perk, Critical behaviour of the two-dimensional Ising susceptibility, Phys. Rev. Lett. 86 (2001) 4120-4123. See also its arXiv preprint cond-mat/0009059 or its preprint in PDF format.
H. Au-Yang, B.-Q. Jin, and J.H.H. Perk, Wavevector-dependent susceptibility in quasiperiodic Ising models, J. Stat. Phys. 102 (2001) 501-543. See also its preprint in PDF format.
H. Au-Yang, B.-Q. Jin, and J.H.H. Perk, Baxter's solution for the free energy of the chiral Potts model, J. Stat. Phys. 102 (2001) 471-499. See also its preprint in PDF format.
H. Au-Yang and J.H.H. Perk, Wavevector-Dependent Susceptibility in Aperiodic Planar Ising Models, in MathPhys Odyssey 2001: Integrable Models and Beyond, M. Kashiwara and T. Miwa, eds., (Birkhäuser, Boston, 2002), pp. 1-21. See also its preprint in PDF format.
H. Au-Yang and J.H.H. Perk, Correlation Functions and Susceptibility in the Z-Invariant Ising Model, in MathPhys Odyssey 2001: Integrable Models and Beyond, M. Kashiwara and T. Miwa, eds., (Birkhäuser, Boston, 2002), pp. 23-48. See also its preprint in PDF format.
H. Au-Yang and J.H.H. Perk, New Results for Susceptibilities in Planar Ising Models, Int. J. Mod. Phys. B 16 (2002) 2089-2095. See also its preprint in PDF format.
H. Au-Yang and J.H.H. Perk, Star-Triangle Equations and Identities in Hypergeometric Series, Int. J. Mod. Phys. B 16 (2002) 1853-1865. See also its preprint in PDF format.
B.-Q. Jin, H. Au-Yang, and J.H.H. Perk, The Three-State Chiral Clock Model, Int. J. Mod. Phys. B 16 (2002) 1979-1986. See also its preprint in PDF format.
J.H.H. Perk, Fa-Yueh Wu, (Conference in honor of Wu's 70th birthday), Int. J. Mod. Phys. B 16, Nos. 14 & 15 (2002) v-xvi. See also its preprint in PDF format.
H. Au-Yang and J.H.H. Perk, Susceptibility Calculations in Periodic and Quasiperiodic Planar Ising Models, Physica A 321 (2003) 81-89. See also its preprint in PDF format.
H. Au-Yang and J.H.H. Perk, Q-dependent Susceptibilities in Z-invariant Pentagrid Ising Models, J. Stat. Phys., 127 (2007) 221-264. See also its arXiv preprint cond-mat/0409557.
H. Au-Yang and J.H.H. Perk, Q-dependent Susceptibilities in Ferromagnetic Quasiperiodic Z-invariant Ising Models, J. Stat. Phys., 127 (2007) 265-286. See also its arXiv preprint cond-mat/0606301.
J.H.H. Perk and H. Au-Yang, Yang-Baxter Equation, in Encyclopedia of Mathematical Physics, eds. J.-P. Françoise, G.L. Naber and Tsou S.T., Oxford: Elsevier, 2006 (ISBN 978-0-1251-2666-3), Vol. 5,, pp. 465-473. See also its extended arXiv preprint math-ph/0606053.
H. Au-Yang and J.H.H. Perk, Overlapping Unit Cells in 3d Quasicrystal Structure, J. Phys. A: Math. Gen. 39 (2006) 9035-9044. See also its arXiv preprint cond-mat/0507117.
J.H.H. Perk and H. Au-Yang, Recent Developments on Ising and Chiral Potts Model, in Differential Geometry and Physics, (Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics), Nankai Tracts in Mathematics, Vol. 10, M.-L. Ge and W. Zhang eds., (World Scientific, Singapore, 2006), pp. 389-398. See also its arXiv preprint math-ph/0606027.
H. Au-Yang and J.H.H. Perk, Quasicrystals: Projections of 5-d Lattice into 2 and 3 Dimensions, in Differential Geometry and Physics, (Proceedings of the 23rd International Conference of Differential Geometric Methods in Theoretical Physics), Nankai Tracts in Mathematics, Vol. 10, M.-L. Ge and W. Zhang eds., (World Scientific, Singapore, 2006), pp. 123-132. See also its arXiv preprint math-ph/0606028.
J.H.H. Perk and H. Au-Yang, Some Recent Results on Pair Correlation Functions and Susceptibilities in Exactly Solvable Models, J. Phys.: Conf. Ser. Vol. 42 (2006) 231-238. See also its arXiv preprint math-ph/0606046.
H. Au-Yang and J.H.H. Perk, Eigenvectors in the Superintegrable Model I: sl₂ Generators, J. Phys. A: Math. Theor. 41 (2008) 275201 (10 pp.). See also its arXiv preprint arXiv:0710.5257.
H. Au-Yang and J.H.H. Perk, Eigenvectors in the Superintegrable Model II: Ground State Sector. J. Phys. A: Math. Theor. 42 (2009) 375208 (16 pp.). See also its arXiv preprint arXiv:0803.3029.
Amit Rai, G. S. Agarwal and J.H.H. Perk, Transport and Quantum Walk of Nonclassical Light in Coupled Waveguides, Phys. Rev. A 78 (2008) 042304 (5 pp.). See also its arXiv preprint arXiv:0807.3063.
J.H.H. Perk and H. Au-Yang, New Results for the Correlation Functions of the Ising Model and the Transverse Ising Chain, J. Stat. Phys. 135 (2009) 599-619. See also its arXiv preprint arXiv:0901.1931.
J.H.H. Perk, Comment on ’Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices’. Phil. Mag. 89 (2009) 761-764. See also its arXiv preprint arXiv:0811.1802.
J.H.H. Perk, Rejoinder to the Response to the Comment on ’Conjectures on exact solution of three-dimensional (3D) simple orthorhombic Ising lattices’. Phil. Mag. 89 (2009) 769-770. See also its arXiv preprint arXiv:0901.2935.
H. Au-Yang and J.H.H. Perk, Identities in the Superintegrable Chiral Potts Model, J. Phys. A: Math. Theor. 43 (2010) 025203 (10 pp.). See also its arXiv preprint arXiv:0906.3153.
H. Au-Yang and J.H.H. Perk, Quantum Loop Subalgebra and Eigenvectors of the Superintegrable Chiral Potts Transfer Matrices. J. Phys. A: Math. Theor. 44 (2011) 025205 (26 pp.). See also its arXiv preprint arXiv:0907.0362.
H. Au-Yang and J.H.H. Perk, Spontaneous Magnetization of the Integrable Chiral Potts Model. J. Phys. A: Math. Theor. 44 (2011) 445005 (20 pp.). See also its arXiv preprint arXiv:1003.4805.
Y. Chan, A.J. Guttmann, B.G. Nickel and J.H.H. Perk, The Ising Susceptibility Scaling Function. J. Stat. Phys. 145 (2011) 549-590. See also its arXiv preprint arXiv:1012.5272.
H. Au-Yang and J.H.H. Perk, Superintegrable chiral Potts model: Proof of the conjecture for the coefficients of the generating function G(t,u). See its arXiv preprint arXiv:1108.4713.
H. Au-Yang and J.H.H. Perk, Serre Relations in the Superintegrable Model. See its arXiv preprint arXiv:1210.5803.
J.H.H. Perk, Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices, Bulletin de la Société des Sciences et des Lettres de Łódż, Série: Recherches sur les Déformations 62 no. 3 (2012) 45-59. See also its arXiv preprint arXiv:1209.0713 (pp. 2-15).
J.H.H. Perk, Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices II. Comment to the Response to “Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices,” Bulletin de la Société des Sciences et des Lettres de Łódż, Série: Recherches sur les Déformations 62 no. 3 (2012) 71-74. See also its arXiv preprint arXiv:1209.0713 (pp. 16-19).
J.H.H. Perk, Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices III. Rejoinder to the 2nd Comment (Rejoinder) to the Comment to the Response to “Erroneous solution of three-dimensional (3D) simple orthorhombic Ising lattices,” Bulletin de la Société des Sciences et des Lettres de Łódż, Série: Recherches sur les Déformations 63 no. 1 (2013) 89-92. See also its arXiv preprint arXiv:1209.0713 (pp. 20-23).
H. Au-Yang and J.H.H. Perk, Quasicrystals—The impact of N.G. de Bruijn. Indagationes Mathematicae 24 (2013) 996-1017. See also its arXiv preprint arXiv:1306.6698.
J.H.H. Perk, Comment on ‘Mathematical structure of the three-dimensional (3D) Ising model’, Chinese Physics B 22 (2013) 080508 (5 pp.). See also its arXiv preprint arXiv:1307.1753.
H. Au-Yang and J.H.H. Perk, Finite-size calculation of eigenvalues in the superintegrable τ₂ model and the degenerate eigenspace, in preparation.
J.H.H. Perk, A simple method to reduce thermodynamic derivatives by computer, arXiv:1401.7728.
H. Au-Yang and J.H.H. Perk, Parafermions in the τ₂ model, J. Phys. A: Math. Theor. 47 (2014) 315002 (19 pp.). See also its arXiv preprint arXiv:1402.0061.
J.H.H. Perk, The Early History of the Integrable Chiral Potts Model and the Odd-Even Problem, J. Phys. A: Math. Theor. 49 (2016) 153001 (20 pp.). See also its arXiv preprint arXiv:1511.08526.
H. Au-Yang and J.H.H. Perk, CSOS models descending from chiral Potts models: Degeneracy of the eigenspace and loop algebra, J. Phys. A: Math. Theor. 49 (2016) 154003 (34 pp.). See also its arXiv preprint arXiv:1511.08523.
M.E. Fisher and J.H.H. Perk, Comments concerning the Ising model and two letters by N.H. March, Phys. Lett. A 380 (2016) 1339-1340. See also its arXiv preprint arXiv:1511.08521.
H. Au-Yang and J.H.H. Perk, About 30 years of integrable chiral Potts model, quantum groups at roots of unity and cyclic hypergeometric functions, Proceedings of the Centre for Mathematics and its Applications, 46 (2017) 4-14. See also its arXiv preprint arXiv:1601.01014.
H. Au-Yang and J.H.H. Perk, Parafermions in the τ₂ model II, arXiv preprint arXiv:1606.06319.
J.H.H. Perk, Onsager algebra and cluster XY-models in a transverse magnetic field, arXiv preprint arXiv:1710.03384.
H. Au-Yang and J.H.H. Perk, Ising Models with Holes: Crossover Behavior, arXiv preprint arXiv:1806.00873.
H. Au-Yang and J.H.H. Perk, Integrable Chiral Potts Model and the Odd-Even Problem in Quantum Groups at Roots of Unity, arXiv preprint arXiv:1806.03359.
H. Au-Yang and J.H.H. Perk, Specific Heat of Ising Models with Holes: Mathematical Details Using Dimer Approaches, arXiv preprint arXiv:1808.07525.
P.J. Forrester, J.H.H. Perk, A.K. Trinh and N.S. Witte, Leading Corrections to the Scaling Function on the Diagonal for the Two-Dimensional Ising Model, J. Stat. Mech.: Theory and Experiment (2019) 023106 (24 pp.). See also its arXiv preprint arXiv:1809.09240.
H. Au-Yang and J.H.H. Perk, Spin-Spin Correlations in Central Rows of Ising Models with Holes, arXiv preprint arXiv:1907.04748.

Last Updated: 11 July, 2019. This page was prepared by Helen Au-Yang and Jacques H.H. Perk.

jhhp@jperk.phy.okstate.edu