The Ising Model on Random Lattices in Arbitrary Dimensions

TL;DR

This paper analyzes the Ising model on random lattices in higher dimensions using tensor models, showing no finite-temperature phase transition and proposing a method for studying critical behavior in such models.

Contribution

It introduces a tensor model approach for analyzing the Ising model on higher-dimensional random lattices and demonstrates the absence of phase transitions at finite temperature.

Findings

No finite-temperature phase transition in 3D and higher

Tensor models generalize matrix models for random surfaces

Method outlined for studying critical behavior in tensor models

Abstract

We study analytically the Ising model coupled to random lattices in dimension three and higher. The family of random lattices we use is generated by the large N limit of a colored tensor model generalizing the two-matrix model for Ising spins on random surfaces. We show that, in the continuum limit, the spin system does not exhibit a phase transition at finite temperature, in agreement with numerical investigations. Furthermore we outline a general method to study critical behavior in colored tensor models.