Random site dilution properties of frustrated magnets on a hierarchical lattice

TL;DR

This paper introduces a method to analyze the magnetic properties of frustrated Ising spin models on hierarchical lattices with random dilution, revealing complex entropy and phase crossover behaviors.

Contribution

It develops a novel recursive approach using replicas to systematically incorporate disorder effects in frustrated magnetic models on hierarchical lattices.

Findings

Presence of macroscopic zero-temperature entropy close to spin-ice estimates

Identification of a crossover to a paramagnetic phase

Numerical evaluation of specific heat and susceptibility

Abstract

We present a method to analyze magnetic properties of frustrated Ising spin models on specific hierarchical lattices with random dilution. Disorder is induced by dilution and geometrical frustration rather than randomness in the internal couplings of the original Hamiltonian. The two-dimensional model presented here possesses a macroscopic entropy at zero temperature in the large size limit, very close to the Pauling estimate for spin-ice on pyrochlore lattice, and a crossover towards a paramagnetic phase. The disorder due to dilution is taken into account by considering a replicated version of the recursion equations between partition functions at different lattice sizes. An analysis at first order in replica number allows for a systematic reorganization of the disorder configurations, leading to a recurrence scheme. This method is numerically implemented to evaluate the thermodynamical quantities such as specific heat and susceptibility in an external field.