Multicritical tensor models and hard dimers on spherical random lattices

TL;DR

This paper introduces new multicritical tensor models that exhibit simple critical behaviors and can be interpreted as models of hard dimers on random spherical lattices in higher dimensions, revealing phase transitions.

Contribution

It presents novel multicritical tensor models with entropy exponents and interprets them as hard dimer models on random lattices, including analysis of phase transitions.

Findings

Identification of multicritical behaviors with entropy exponents b3 = (m-1)/m

Interpretation of tensor interactions as hard dimers with dimer activities

Description of a phase transition between dilute and crystallized phases

Abstract

Random tensor models which display multicritical behaviors in a remarkably simple fashion are presented. They come with entropy exponents \gamma = (m-1)/m, similarly to multicritical random branched polymers. Moreover, they are interpreted as models of hard dimers on a set of random lattices for the sphere in dimension three and higher. Dimers with their exclusion rules are generated by the different interactions between tensors, whose coupling constants are dimer activities. As an illustration, we describe one multicritical point, which is interpreted as a transition between the dilute phase and a crystallized phase, though with negative activities.