Real-Space Renormalization Group Study of the Two-dimensional Blume-Capel Model with a Random Crystal Field

TL;DR

This study uses real-space renormalization group methods to analyze the phase diagram of the two-dimensional Blume-Capel model with random crystal fields, revealing continuous transitions and universality class changes at zero temperature.

Contribution

It provides a detailed RG analysis of the disordered Blume-Capel model, showing the persistence of continuous transitions and identifying the zero-temperature universality class.

Findings

All randomness levels show Ising-like continuous transitions.

No first-order transitions are observed with randomness.

Zero-temperature transition belongs to the percolation fixed point universality class.

Abstract

The phase-diagram of the two-dimensional Blume-Capel model with a random crystal field is investigated within the framework of a real-space renormalization group approximation. Our results suggest that, for any amount of randomness, the model exhibits a line of Ising-like continuous transitions, as in the pure model, but no first-order transition. At zero temperature the transition is also continuous, but not in the same universality class as the Ising model. In this limit, the attractor (in the renormalization group sense) is the percolation fixed point of the site diluted spin-1/2 Ising model. The results we found are in qualitative agreement with general predictions made by Berker and Hui on the critical behaviour of random models.