On the spin interface distribution for non-integrable variants of the two-dimensional Ising model

TL;DR

This paper extends the construction of a martingale observable for the 2D Ising model's spin interface to non-integrable variants, suggesting the interface's scaling limit remains SLE(3) under certain conjectures.

Contribution

It introduces a Grassmann integral formulation for non-integrable Ising variants and conjectures their interface scaling limit matches the integrable case.

Findings

Martingale observable construction extends to non-integrable models

Conjecture that the interface scaling limit is SLE(3)

Potential universality of the interface distribution at criticality

Abstract

We point out that the construction of a martingale observable describing the spin interface of the two-dimensional Ising model extends to a class of non-integrable variants of the two-dimensional Ising model, and express it in terms of Grassmann integrals. Under a conjecture about the scaling limit of this object, which is similar to some results recently obtained using constructive renormalization group methods, this would imply that the distribution of the interface at criticality has the same scaling limit as in the integrable model: Schramm-Loewner evolution SLE(3).