Frustration -- Exactly Solved Frustrated Models

TL;DR

This paper reviews exactly solvable two-dimensional frustrated Ising models, highlighting their complex phenomena like high degeneracy, multiple phases, and reentrant transitions, and discusses similar effects in non-solvable models.

Contribution

It provides a comprehensive analysis of exactly solvable frustrated spin systems and discusses their complex behaviors and implications for non-solvable models.

Findings

High ground-state degeneracy observed

Multiple phase transitions identified

Reentrant behavior and disorder lines discussed

Abstract

After a short introduction on frustrated spin systems, we study in this chapter several two-dimensional frustrated Ising spin systems which can be exactly solved by using vertex models. We show that these systems contain most of the spectacular effects due to the frustration: high ground-state degeneracy, existence of several phases in the ground-state phase diagram, multiple phase transitions with increasing temperature, reentrance, disorder lines, partial disorder at equilibrium. Evidences of such effects in non solvable models are also shown and discussed.