We show this configuration in Figure 1. We calculate that the energy of this configuration is HΛ(σ|σ) = 0. We can calculate the energy of this configuration in a different way, using line segments separating lattice points with different spins, as follows. For an n × n square, there are 2n(n + 1) nearest neighbor interactions. Put a line segment between every two lattice points with different s...

We derive the Wulff construction for Kac Ising models with long but finite range interaction in dimensions d > 2. Some open problems concerning the phase coexistence for more general models are also discussed.

We give a mathematical theory of the wetting phenomenon in the 2D Ising model using the formalism of Gibbs states. We treat the grand canonical and canonical ensembles.

We study the type II string theories compactified on manifolds of G2 holonomy of the type (Calabi-Yau 3-fold×S)/Z2 where CY3 sectors realized by the Gepner models. We construct modular invariant partition functions for G2 manifold for arbitrary Gepner models of the Calabi-Yau sector. We note that the conformal blocks contain the tricritical Ising model and find extra massless states in the twis...

JBSTRACT In the real algebra R(G) over a certain finite group, the operator exp is defined. A condition is stated on exp J which is necessary and sufficient for J in R(G) to be nonnegative (where J is viewed as a function G + R). Physically, this amounts to a condition on the correlations of a generalized system of Ising spins which is necessary and sufficient for the ferromagnetism of the system.

We study the finite temperature features of the thermodynamical observables of the Ising model with mixed perturbation.

The hyperensembles, introduced by Crooks in a context of non-equilibrium statistical physics, are considered here as a tool for systems in equilibrium. Simple examples like the ideal gas, the mean-field model, and the Ising interaction on small square lattices, are worked out to illustrate the concepts.

Using an effective field theory with correlations we study a diluted mixed spin-112 and spin-312 Ising ferrimagnetic system with a crystal field interaction D(D < 0) on a honeycomb lattice. We find that the system may exhibit two compensation points in the total magnetization curve, although the corresponding system in the absence of dilution or with D = 0 never exhibits any compensation point ...