Phase Transitions in Disordered Systems

TL;DR

This paper investigates phase transitions in disordered systems through theoretical and numerical methods, including renormalization group analysis and large-scale simulations, revealing new insights into the behavior of diluted models across multiple dimensions.

Contribution

It introduces a new finite size scaling formulation within the microcanonical ensemble and provides comprehensive numerical results on diluted models in various dimensions.

Findings

Microcanonical simulations reveal first-order behavior in 3D diluted Potts model.

Large-scale simulations confirm self-averaging in 3D diluted Heisenberg model.

FSS analysis of 4D diluted Ising model clarifies conflicting theories.

Abstract

We face the problem of phase transitions in diluted systems both from theoretical and numerical sides. We study the effects of quenched site-dilution in classical models (Heisenberg, Ising and Potts) in 2, 3, and 4 dimensions both by using the Renormalization Group and numerical simulations in the canonical and microcanonical ensembles. We propose and check a new formulation of the Finite Size Scaling ansatz (FSS) inside the microcanonical ensemble. We use microcanonical simulations to obtain a clear fist-order behavior for the diluted Potts model in 3D, estimating the tricritical dilution. We perform large-scale simulations of the 3D diluted Heisenberg model, checking its self-averaging properties. Finally we study the 4D diluted Ising model obtaining from the FSS of the specific heat a clear differentiation between the existing conflicting theories. We also compiled a large number of appendix that we expect to be used as future reference.