# Stability of uniqueness and coexistence of equilibrium states of the Ising model under long range perturbations

@inproceedings{Usuki2021StabilityOU, title={Stability of uniqueness and coexistence of equilibrium states of the Ising model under long range perturbations}, author={Shunsuke Usuki}, year={2021} }

. In this paper, we study perturbations of the d -dimensional Ising model for d ≥ 2, including long range ones to which the Pirogov-Sinai theory is not applicable. We show that the uniqueness of the equilibrium state of the Ising model at high temperature and the coexistence of equilibrium states at low temperature are preserved by spin-ﬂip symmetric perturbations.

## References

SHOWING 1-10 OF 22 REFERENCES

Differentiability properties of the pressure in lattice systems

- Mathematics
- 1980

In two recent papers Ruelle gave a heuristic theory of phase transitions, using some techniques introduced by Israel. He proves a version of Gibbs phase rule, assuming a differentiability condition…

A note on the stability of phase diagrams in lattice systems

- Mathematics
- 1981

We construct a class of non-symmetry breaking pair interactions, which change the phase diagram of then.n. Ising and classicalX Y model. Furthermore we improve earlier obtained constraints on the…

More surprises in the general theory of lattice systems

- Mathematics
- 1982

I use Israel's methods to prove new theorems of “ubiquitous pathology” for classical and quantum lattice systems. The main result is the following: Let Φ be any interaction and ϱ be any…

Generic triviality of phase diagrams in spaces of long-range interactions

- Mathematics
- 1986

We show that interactions with multiple translation-invariant equilibrium states form a very “thin” set in spaces of long-range interactions of classical or quantum lattice systems. For example,…

Condensation of lattice gases

- Mathematics
- 1966

Techniques due toR. L. Dobrushin andR. Griffiths are combined to prove the existence of a first order phase transition at low temperature for a class of lattice systems with non nearest-neighbour…

An alternate version of Pirogov-Sinai theory

- Physics
- 1984

A new approach to the Pirogov-Sinai theory of phase transitions is developed, not employing the contour models with a parameter. The completeness of the phase diagram is proven.

Translation invariance and instability of phase coexistence in the two dimensional Ising system

- Mathematics
- 1980

It is shown that any Gibbs state of the two dimensional ferromagnetic Ising system is of the form λμ++(1−λ)μ−, with some λ∈ [0, 1]. This excludes the possibility of a locally stable phase coexistence…

Statistical Mechanics of Lattice Systems: A Concrete Mathematical Introduction

- Computer Science
- 2017

Extension of Pirogov-Sinai theory of phase transitions to infinite range interactions. II. Phase diagram

- Mathematics
- 1988

This paper is the second part of our attempt of an extension of the Pirogov-Sinai theory of phase transitions at low temperatures, applicable to the lattice spin systems with finite range…