Classical Phase Transitions of Geometrically Constrained O($N$) Spin Systems

TL;DR

This paper investigates phase transitions in various constrained O(N) spin systems, analyzing critical behavior and fixed points using a unified Ginzburg-Landau approach, and explores the effects of softened constraints and defects.

Contribution

It introduces a unified formalism for analyzing phase transitions in different constrained O(N) models, including novel spin-plaquette systems, and computes critical exponents via epsilon expansion.

Findings

Stable fixed points exist for large N.

Softened constraints and defects significantly affect phase stability.

Critical exponents are systematically calculated.

Abstract

We study the phase transition between the high temperature algebraic liquid phase and the low temperature ordered phase in several different types of locally constrained O(N) spin systems, using a unified constrained Ginzburg-Landau formalism. The models we will study include: 1, O(N) spin-ice model with cubic symmetry; 2, O(N) spin-ice model with easy-plane and easy-axis anisotropy; 3, a novel O(N) "spin-plaquette" model, with a very different local constraint from the spin-ice. We calculate the renormalization group equations and critical exponents using a systematic \epsilon = 4 - d expansion with constant N, stable fixed points are found for large enough N. In the end we will also study the situation with softened constraints, the defects of the constraints will destroy the algebraic phase and play an important role at all the transitions.