High-precision phase diagram of spin glasses from duality analysis with real-space renormalization and graph polynomials

TL;DR

This paper introduces a duality-based method with real-space renormalization and graph polynomials to accurately determine the phase diagrams of two-dimensional spin glasses, achieving high precision and convergence.

Contribution

The authors develop a novel duality analysis technique that systematically improves the accuracy of spin glass phase diagrams using finite basis computations.

Findings

Precise location of the Nishimori point at p_N = 0.10929 ± 0.00002.

High-temperature phase diagram features are accurately captured.

Analytical proof of the finite critical point in the ground state.

Abstract

We propose a duality analysis for obtaining the critical manifold of two-dimensional spin glasses. Our method is based on the computation of quenched free energies with periodic and twisted periodic boundary conditions on a finite basis. The precision can be systematically improved by increasing the size of the basis, leading to very fast convergence towards the thermodynamic limit. We apply the method to obtain the phase diagrams of the random-bond Ising model and $q$-state Potts gauge glasses. In the Ising case, the Nishimori point is found at $p_N = 0.10929 \pm 0.00002$, in agreement with and improving on the precision of existing numerical estimations. Similar precision is found throughout the high-temperature part of the phase diagram. Finite-size effects are larger in the low-temperature region, but our results are in qualitative agreement with the known features of the phase diagram. In particular we show analytically that the critical point in the ground state is located at finite $p_0$.