Kramers-Wannier Duality and Random Bond Ising Model

2023/06/04 by Song, Chaoming · 1 citation
#Disordered Systems and Neural Networks (cond-mat.dis-nn) #FOS: Physical sciences #Statistical Mechanics (cond-mat.stat-mech)

paper · doi:10.48550/arxiv.2306.02220

Abstract

We present a new combinatorial approach to the Ising model incorporating arbitrary bond weights on planar graphs. In contrast to existing methodologies, the exact free energy is expressed as the determinant of a set of ordered and disordered operators defined on vertices and dual vertices respectively, thereby explicitly demonstrating the Kramers-Wannier duality. The implications of our derived formula for the random bond Ising model are further elucidated.

Cited by

• Ising on the donut: Regimes of topological quantum error correction from statistical mechanics

Related

• On bond anisotropy for the ising model through the geometry of numbers
• Duality and even number spin-correlation functions in the two dimensional square lattice ising model
• On thermodynamic states of the Ising model on scale-free graphs
• The near critical random bond ising model via embedding deformation
• Exact statistical mechanics of the Ising model on networks