Scaling and universality in the phase diagram of the 2D Blume-Capel model

Johannes Zierenberg, Nikolaos G. Fytas, Martin Weigel, Wolfhard Janke, Anastasios Malakis

Research output: Contribution to journalArticle

13 Citations (Scopus)
10 Downloads (Pure)

Abstract

We review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of $\xi/L$ with the exactly known result for the Ising universality class.

Publisher Statement: The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60337-x
Original languageEnglish
Pages (from-to)789-804
Number of pages16
JournalThe European Physical Journal Special Topics
Volume226
DOIs
Publication statusPublished - 5 Apr 2017

Fingerprint

Phase diagrams
phase diagrams
scaling
Phase boundaries
simulation
Monte Carlo simulation

Keywords

  • cond-mat.stat-mech

Cite this

Scaling and universality in the phase diagram of the 2D Blume-Capel model. / Zierenberg, Johannes; Fytas, Nikolaos G.; Weigel, Martin; Janke, Wolfhard; Malakis, Anastasios.

In: The European Physical Journal Special Topics, Vol. 226, 05.04.2017, p. 789-804.

Research output: Contribution to journalArticle

@article{99e0ce7f72b84522a006c17e4f4ef4ea,
title = "Scaling and universality in the phase diagram of the 2D Blume-Capel model",
abstract = "We review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of $\xi/L$ with the exactly known result for the Ising universality class.Publisher Statement: The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60337-x",
keywords = "cond-mat.stat-mech",
author = "Johannes Zierenberg and Fytas, {Nikolaos G.} and Martin Weigel and Wolfhard Janke and Anastasios Malakis",
year = "2017",
month = "4",
day = "5",
doi = "10.1140/epjst/e2016-60337-x",
language = "English",
volume = "226",
pages = "789--804",
journal = "European Physical Journal: Special Topics",
issn = "1951-6355",
publisher = "EDP Sciences",

}

TY - JOUR

T1 - Scaling and universality in the phase diagram of the 2D Blume-Capel model

AU - Zierenberg, Johannes

AU - Fytas, Nikolaos G.

AU - Weigel, Martin

AU - Janke, Wolfhard

AU - Malakis, Anastasios

PY - 2017/4/5

Y1 - 2017/4/5

N2 - We review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of $\xi/L$ with the exactly known result for the Ising universality class.Publisher Statement: The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60337-x

AB - We review the pertinent features of the phase diagram of the zero-field Blume-Capel model, focusing on the aspects of transition order, finite-size scaling and universality. In particular, we employ a range of Monte Carlo simulation methods to study the 2D spin-1 Blume-Capel model on the square lattice to investigate the behavior in the vicinity of the first-order and second-order regimes of the ferromagnet-paramagnet phase boundary, respectively. To achieve high-precision results, we utilize a combination of (i) a parallel version of the multicanonical algorithm and (ii) a hybrid updating scheme combining Metropolis and generalized Wolff cluster moves. These techniques are combined to study for the first time the correlation length of the model, using its scaling in the regime of second-order transitions to illustrate universality through the observed identity of the limiting value of $\xi/L$ with the exactly known result for the Ising universality class.Publisher Statement: The final publication is available at Springer via http://dx.doi.org/10.1140/epjst/e2016-60337-x

KW - cond-mat.stat-mech

U2 - 10.1140/epjst/e2016-60337-x

DO - 10.1140/epjst/e2016-60337-x

M3 - Article

VL - 226

SP - 789

EP - 804

JO - European Physical Journal: Special Topics

JF - European Physical Journal: Special Topics

SN - 1951-6355

ER -