Universality from disorder in the random-bond Blume-Capel model

N. G. Fytas, J. Zierenberg, P. E. Theodorakis, M. Weigel, W. Janke, A. Malakis

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Abstract

Using high-precision Monte Carlo simulations and finite-size scaling we study the effect of quenched disorder in the exchange couplings on the Blume-Capel model on the square lattice. The first-order transition for large crystal-field coupling is softened to become continuous, with a divergent correlation length. An analysis of the scaling of the correlation length as well as the susceptibility and specific heat reveals that it belongs to the universality class of the Ising model with additional logarithmic corrections observed for the Ising model itself if coupled to weak disorder. While the leading scaling behavior in the disordered system is therefore identical between the second-order and first-order segments of the phase diagram of the pure model, the finite-size scaling in the ex-first-order regime is affected by strong transient effects with a crossover length scale $L^{\ast} \approx 32$ for the chosen parameters.
Original languageEnglish
Article number040102
Number of pages6
JournalPhysical review E: Statistical, Nonlinear, and Soft Matter Physics
Volume97
Issue number4
DOIs
Publication statusPublished - 13 Apr 2018

Fingerprint

Blume-Capel Model
Universality
Disorder
Finite-size Scaling
disorders
Correlation Length
First-order
scaling
Ising Model
Ising model
Quenched Disorder
Disordered Systems
Specific Heat
Scaling Behavior
Square Lattice
Length Scale
Susceptibility
Phase Diagram
Crossover
Logarithmic

Bibliographical note

6 pages, 4 figures, version to be published in Phys. Rev. E as a Rapid Communication

Keywords

  • cond-mat. dis-nn

Cite this

Universality from disorder in the random-bond Blume-Capel model. / Fytas, N. G.; Zierenberg, J.; Theodorakis, P. E.; Weigel, M.; Janke, W.; Malakis, A.

In: Physical review E: Statistical, Nonlinear, and Soft Matter Physics, Vol. 97, No. 4, 040102, 13.04.2018.

Research output: Contribution to journalArticle

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AU - Janke, W.

AU - Malakis, A.

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