Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of the Physical Society of Japan

Free Energies and Critical Exponents of the A1(1), B n(1), C n(1) and D n(1) Face Models

Murray T. Batchelor, V. Fridkin, Atsuo Kuniba, Kazumitsu Sakai, Y. -K. Zhou

Published Jul 15, 1997• 0 citations
Publisher

Abstract

We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation.The models considered are related to the affine Lie algebrasn and D(1) n .The bulk and surface specific heat exponents are seen to satisfy the scaling relation 2α s = α b + 2. It follows from scaling relations that in regime III the correlation length exponent ν is given by ν = (l + g)/2g, where l is the level and g is the dual Coxeter number.In regime II we find ν = (l + g)/2l.

DOI
10.1143/jpsj.66.2208

Related papers

Free Energies and Critical Exponents of theA1(1),Bn(1),Cn(1)andDn(1)Face Models

Murray T. Batchelor, V. Fridkin, Atsuo Kuniba +2 more

We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation.The models considered are related to the affine Lie algebras A (1)

arXiv:cond-mat/9703036•Journal of the Physical Society of Japan•Apr 1, 1997•5 citations

The critical exponents of Ising model systems with pure three-body interactions. III

David W. Wood, H P Griffiths

For pt. II, see abstr. A64455 of 1973. The critical-point exponents of two Ising models with pure three-spin coupling terms are examined using low-temperature (T<T c ) series expansions for the thermodynamic functions. In particular the critical isotherm exponent delta is examined by applying numerical extrapolation methods to the critical isotherm. The two models are (a) a two-dimensional triangular lattice and (b) a three-dimensional face-centred cubic lattice. Direct numerical estimates of alpha ', beta and delta for (b) show that the scaling relations hold for this model and it is found that alpha '=0.655, beta =0.0538, gamma =1.24, nu =0.448, eta =-0.76, and delta =24 on the basis of the scaling relations. The numerical accuracy of the exponents beta and delta for model (a) does not permit an independent verification of the scaling relations; assuming scaling to hold here also, and using the exact result alpha '= 2 / 3 obtained by Baxter and Wu, it is found that gamma '=1.187+or-0.006, nu = 2 / 3 , eta =0.219+or-0.009, beta =0.073+or-0.003, and delta =17.3+or-0.8.

Journal of Physics C Solid State Physics•Apr 21, 1974•19 citations

Surface free energies, interfacial tensions and correlation lengths of the ABF models

David O’Brien, Paul A. Pearce

The surface free energies, interfacial tensions and correlation lengths of the Andrews - Baxter - Forrester models in regimes III and IV are calculated with fixed boundary conditions. The interfacial tensions are calculated between arbitrary phases and are shown to be additive. The associated critical exponents are given by with in regime III and with in regime IV. Our results are obtained using general commuting transfer matrix and inversion relation methods that may be applied to other solvable lattice models.

arXiv:cond-mat/9511081•Journal of Physics A Mathematical and General•Apr 7, 1997•22 citations

An Ising model in a magnetic field with a boundary

Murray T. Batchelor, V. Fridkin, Y-K Zhou

We obtain the diagonal reflection matrices for a recently introduced family of dilute lattice models in which the model can be viewed as an Ising model in a magnetic field. We calculate the surface free energy from the crossing-unitarity relation and thus directly obtain the critical magnetic surface exponent for L odd and surface specific heat exponent for L even in each of the various regimes. For L = 3 in the appropriate regime we obtain the Ising exponent , which is the first determination of this exponent without the use of scaling relations.

arXiv:cond-mat/9511090•Journal of Physics A Mathematical and General•Feb 21, 1996•15 citations

1 New Estimates On Various Critical/Universal Quantities of the 3D Ising Model ∗

Martin Hasenbusch B, K. Pinn, Universität Münster

We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi**3, where fs is the singular part of the free energy.

•Jan 1, 1997•1 citation

Exact solution and surface critical behaviour of open cyclic SOS lattice models

Yu‐Kui Zhou, Murray T. Batchelor

We consider the L-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions. The eigenspectra of the unfused transfer matrix is obtained from the functional relations using the analytic Bethe ansatz. For a special case of crossing parameter , the finite-size corrections to the eigenspectra of the critical models are obtained, from which the corresponding conformal dimensions follow. The calculation of the surface free energy away from criticality yields two surface specific heat exponents, and , where coprime to L. These results are in agreement with the scaling relations and .

arXiv:cond-mat/9602078•Journal of Physics A Mathematical and General•May 7, 1996•9 citations
We obtain the free energies and critical exponents of models associated with elliptic solutions of the star-triangle relation and reflection equation.The models considered are related to the affine Lie algebrasn and D(1) n .The bulk and surface specific heat exponents are seen to satisfy the scaling relation 2α s = α b + 2. It follows from scaling relations that in regime III the correlation length exponent ν is given by ν = (l + g)/2g, where l is the level and g is the dual Coxeter number.In regime II we find ν = (l + g)/2l.
For pt. II, see abstr. A64455 of 1973. The critical-point exponents of two Ising models with pure three-spin coupling terms are examined using low-temperature (T<T c ) series expansions for the thermodynamic functions. In particular the critical isotherm exponent delta is examined by applying numerical extrapolation methods to the critical isotherm. The two models are (a) a two-dimensional triangular lattice and (b) a three-dimensional face-centred cubic lattice. Direct numerical estimates of alpha ', beta and delta for (b) show that the scaling relations hold for this model and it is found that alpha '=0.655, beta =0.0538, gamma =1.24, nu =0.448, eta =-0.76, and delta =24 on the basis of the scaling relations. The numerical accuracy of the exponents beta and delta for model (a) does not permit an independent verification of the scaling relations; assuming scaling to hold here also, and using the exact result alpha '= 2 / 3 obtained by Baxter and Wu, it is found that gamma '=1.187+or-0.006, nu = 2 / 3 , eta =0.219+or-0.009, beta =0.073+or-0.003, and delta =17.3+or-0.8.
The surface free energies, interfacial tensions and correlation lengths of the Andrews - Baxter - Forrester models in regimes III and IV are calculated with fixed boundary conditions. The interfacial tensions are calculated between arbitrary phases and are shown to be additive. The associated critical exponents are given by with in regime III and with in regime IV. Our results are obtained using general commuting transfer matrix and inversion relation methods that may be applied to other solvable lattice models.
We obtain the diagonal reflection matrices for a recently introduced family of dilute lattice models in which the model can be viewed as an Ising model in a magnetic field. We calculate the surface free energy from the crossing-unitarity relation and thus directly obtain the critical magnetic surface exponent for L odd and surface specific heat exponent for L even in each of the various regimes. For L = 3 in the appropriate regime we obtain the Ising exponent , which is the first determination of this exponent without the use of scaling relations.
We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi**3, where fs is the singular part of the free energy.
We consider the L-state cyclic solid-on-solid lattice models under a class of open boundary conditions. The integrable boundary face weights are obtained by solving the reflection equations. Functional relations for the fused transfer matrices are presented for both periodic and open boundary conditions. The eigenspectra of the unfused transfer matrix is obtained from the functional relations using the analytic Bethe ansatz. For a special case of crossing parameter , the finite-size corrections to the eigenspectra of the critical models are obtained, from which the corresponding conformal dimensions follow. The calculation of the surface free energy away from criticality yields two surface specific heat exponents, and , where coprime to L. These results are in agreement with the scaling relations and .