Generalized codes and their application to Ising models with four-spin interactions including the eight-vertex model
- 1 September 1974
- journal article
- Published by IOP Publishing in Journal of Physics A: Mathematical, Nuclear and General
- Vol. 7 (13) , 1596-1612
- https://doi.org/10.1088/0305-4470/7/13/014
Abstract
Generalized codes are defined for the simple quadratic lattice and it is shown how they may be used to derive high magnetic field or low temperature expansions for two Ising-type models with four-spin interactions. One of these models, namely Baxter's eight-vertex model, has critical exponents which are known to depend on x, the ratio of the strengths of the four-spin to two-spin interactions. The series so derived are analysed to yield estimates of the critical exponent delta for the magnetization as a function of magnetic field at Tc. The results for both models are consistent with a constant value delta =15 independent of x as predicted by the scaling laws.Keywords
This publication has 28 references indexed in Scilit:
- Critical polarization of the eight-vertex modelJournal of Physics A: Mathematical, Nuclear and General, 1974
- Exact Solution of an Ising Model with Three-Spin Interactions on a Triangular LatticePhysical Review Letters, 1973
- On the spontaneous order of the eight-vertex modelJournal of Physics C: Solid State Physics, 1973
- Comment on 'Critical exponents for the modified F model'Journal of Physics C: Solid State Physics, 1973
- Critical exponents of the modified F modelJournal of Physics C: Solid State Physics, 1973
- Estimates for the critical index of the susceptibility for Baxter's model as a function of a parameterPhysics Letters A, 1972
- Partition function of the Eight-Vertex lattice modelAnnals of Physics, 1972
- Critical Point Behavior of the Ising Model with Higher-Neighbor Interactions PresentJournal of Mathematical Physics, 1969
- Ising Model with Second-Neighbor Interaction. I. Some Exact Results and an Approximate SolutionPhysical Review B, 1969
- The theory of equilibrium critical phenomenaReports on Progress in Physics, 1967