Phase Transitions with Four-Spin Interactions

Phase Transitions with Four-Spin Interactions

Using an extended Lee-Yang theorem and GKS correlation inequalities, we prove, for a class of ferromagnetic multi-spin interactions, that they will have a phase transition (and spontaneous magnetization) if, and only if, the external field h = 0 (and the temperature is low enough). We also show the absence of phase transitions for some nonferromagnetic interactions. The FKG inequalities are sho...

Quantum phase transitions in the transverse one-dimensional Ising model with four-spin interactions

Phase Transitions for the Potts Model with Four Competing Interactions

In this paper we study phase transitions for the Potts model with four competing interactions (external field, the nearest neighbor, the second neighbors and triples of neighbors) on Cayley tree of order two. We prove that for some parameter values of the model there is phase transition. We reduce the problem of describing limiting Gibbs measures to the problem of solving a system of nonlinear ...

Phase Transitions in Quantum Spin Systems with Isotropic and Nonisotropic Interactions

A basic subtlety in the study of statistical mechanics is the following: In nature, we observe abrupt changes in certain basic physical quantities, such as the magnetization of a magnet, but the statistical mechanics of systems with finitely many degrees of freedom is typically real analytic in all external variables. The resolution of this apparent paradox is that the abrupt changes are only a...

Dynamical Phase Transitions and Spin Glasses

By measuring the distance between two configurations subjected to the same thermal noise, one observes for spin glasses three phases: a high-temperature phase (T> T 1), where the distance between the two configurations vanishes in the long-time limit; an intermediate phase (1’~< T < T,), where this distance has a nonzero limit independent of the initial distance; a low-temperature phase (T< ~‘2...