The effect of quenched bond disorder on first-order phase transitions

Abstract

We investigate the effect of quenched bond disorder on the two-dimensional three-color Ashkin-Teller model, which undergoes a first-order phase transition in the absence of impurities. This is one of the simplest and striking models in which quantitative numerical simulations can be carried out to investigate emergent criticality due to disorder rounding of first-order transition. Utilizing extensive cluster Monte Carlo simulations on large lattice sizes of up to $128\times 128$ spins, each of which is represented by three colors taking values $\pm 1$, we show that the rounding of the first-order phase transition is an emergent criticality. We further calculate the correlation length critical exponent, $\nu$, and the magnetization critical exponent, $\beta$, from finite size scaling analysis. We find that the critical exponents, $\nu$ and $\beta$, change as the strength of disorder or the four-spin coupling varies, and we show that the critical exponents appear not to be in the Ising universality class. We know of no analytical approaches that can explain our non-perturbative results. However our results should inspire further work on this important problem, either numerical or analytical.

arXiv comment8 pages, 11 figures; the simulations are now extended to 128x128 lattice with three colors of the Ashvin-Teller model

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Cited by in corpus (8)

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• Theory of Driven Nonequilibrium Critical Phenomena
• Emerging criticality in the disordered three-color Ashkin-Teller model
• Absence of first order transition in the random crystal field Blume-Capel model on a fully connected graph
• Activated scaling in disorder rounded first-order quantum phase transitions
• Nonuniversality in random criticality
• Emerging critical behavior at a first-order phase transition rounded by disorder
• Wetting transition in the McCoy-Wu model