Emergence of the 3D diluted Ising model universality class in a mixture of two magnets

Abstract

Usually, the impact of structural disorder on the magnetic phase transition in the 3D Ising model is analyzed within the framework of quenched dilution by a non-magnetic component, where some lattice sites are occupied by Ising spins, while others are non-magnetic. This kind of quenched dilution, according to the Harris criterion, leads to a change in the critical exponents that govern the asymptotics in the vicinity of the phase transition point. However, the inherent reason for the emergence of a new, random Ising model universality class is not the presence of a non-magnetic component but the disorder in structure of spin arrangement. To demonstrate this fact, in this paper, we set up extensive Monte Carlo simulations of a random mixture of two Ising-like magnets that differ in spin length $s$ and concentration $c$. In doing so, we analyze the effect of structural disorder \textit{per se} without appealing to the presence of a non-magnetic component. We support our numerical simulations with renormalization group calculations. Our results demonstrate the emergence of the 3D randomly diluted Ising model universality class in a random mixture of two Ising magnets. While the asymptotic critical exponents coincide with those known for the site-diluted 3D Ising model, the effective critical behavior is triggered by parameters $s$ and $c$. The impact of their interplay is a subject of detailed analysis.

arXiv commentFinal version published in PRE. 13 pages, 7 figures

References in corpus (27)

• Critical Phenomena and Renormalization-Group Theory
• Bounds on 4D Conformal and Superconformal Field Theories
• Critical exponents of the three dimensional diluted Ising model
• Pushing the Limits of Monte Carlo Simulations for the 3d Ising Model
• Lack of Self-Averaging in Critical Disordered Systems
• Randomly dilute spin models: a six-loop field-theoretic study
• Critical behavior of O(2)xO(N) symmetric models
• New Universality Class in three dimensions: the Antiferromagnetic $R{P}^2$ model
• Universality class of 3D site-diluted and bond-diluted Ising systems
• The four dimensional site-diluted Ising model: a finite-size scaling study
• Six-loop $\epsilon$ expansion study of three-dimensional $n$-vector model with cubic anisotropy
• The three-dimensional randomly dilute Ising model: Monte Carlo results
• About the relevance of the fixed dimension perturbative approach to frustrated magnets in two and three dimensions
• Weak quenched disorder and criticality: resummation of asymptotic(?) series
• Summability of the perturbative expansion for a zero-dimensional disordered spin model
• Calculations of the dynamical critical exponent using the asymptotic series summation method
• Universality in disordered systems: The case of the three-dimensional random-bond Ising model
• Crossover behavior in three-dimensional dilute spin systems
• Analysis of the 3d massive renormalization group perturbative expansions: a delicate case
• Fixed points in frustrated magnets revisited
• Generalized Ising Model on a Scale-Free Network: An Interplay of Power Laws
• Ising model with variable spin/agent strengths
• Critical behavior of weakly disordered Ising model: Six-loop $\sqrt{\epsilon }$ expansion study
• SWAP algorithm for lattice spin models
• Effective and asymptotic criticality of structurally disordered magnets
• Criticality of the random-site Ising model: Metropolis, Swendsen-Wang and Wolff Monte Carlo algorithms
• Ising model with varying spin strength on a scale-free network: scaling functions and critical amplitude ratios

Cited by in corpus (1)

• Effective and asymptotic scaling in a one-dimensional billiard problem