By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+ϵ$ dimensions. We found that the long-length-scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $\ensuremath{\sigma}$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at $T=0$ ; therefore the uncertainty in the phase diagram of this model is removed.By considering the appropriate finite-size effect, we explain the connection between Monte Carlo simulations of two-dimensional anisotropic Heisenberg antiferromagnet in a field and the early renormalization group calculation for the bicritical point in $2+ϵ$ dimensions. We found that the long-length-scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $\ensuremath{\sigma}$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at $T=0$; therefore the uncertainty in the phase diagram of this model is removed.

arXiv:cond-mat/0607250Physical Review BAug 11, 200616 citations

Finite-size scaling of driven diffusive systems: Theory and Monte Carlo studies

Kwan-tai Leung

By identifying anisotropic scaling as the dominant feature of a lattice gas driven by a strong electric field, I obtain finite-size scaling forms by extending exact field-theoretic results. These are texted and supplemented by extensive Monte Carlo simulations in two dimensons. Excellent agreements are found. This resolves the disagreements between simulations and theories on the universality of the related models. Novel features of the finite-size effects of intrinsically anisotropic systems are emphasized.By identifying anisotropic scaling as the dominant feature of a lattice gas driven by a strong electric field, I obtain finite-size scaling forms by extending exact field-theoretic results. These are texted and supplemented by extensive Monte Carlo simulations in two dimensons. Excellent agreements are found. This resolves the disagreements between simulations and theories on the universality of the related models. Novel features of the finite-size effects of intrinsically anisotropic systems are emphasized.

Physical Review LettersJan 1, 1991104 citations

Scaling Theory for Finite-Size Effects in the Critical Region

Michael Ellis Fisher, Michael N. Barber

Current physics sources and commentsJan 1, 19882 citations

NONUNIVERSAL FINITE-SIZE EFFECTS NEAR CRITICAL POINTS

V. Dohm

International Conference on Path IntegralsNov 1, 20080 citations

Finite-size scaling study of the two-dimensional Blume-Capel model

Paul D. Beale

The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point ( ${T}_{t}$ =0.610\ifmmode\pm\else\textpm\fi{}0.005, ${D}_{t}$ =1.9655\ifmmode\pm\else\textpm\fi{}0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.The phase diagram of the two-dimensional Blume-Capel model is investigated by using the technique of phenomenological finite-size scaling. The location of the tricritical point and the values of the critical and tricritical exponents are determined. The location of the tricritical point (${T}_{t}$=0.610\ifmmode\pm\else\textpm\fi{}0.005, ${D}_{t}$=1.9655\ifmmode\pm\else\textpm\fi{}0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.

Physical review. B, Condensed matterFeb 1, 1986119 citations

2+ϵ

dimensions. We found that the long-length-scale physics of the Monte Carlo simulations is indeed captured by the anisotropic nonlinear $\ensuremath{\sigma}$ model. Our Monte Carlo data and analysis confirm that the bicritical point in two dimensions is Heisenberg-like and occurs at

T=0

; therefore the uncertainty in the phase diagram of this model is removed.

{T}_{t}

=0.610\ifmmode\pm\else\textpm\fi{}0.005,

{D}_{t}

=1.9655\ifmmode\pm\else\textpm\fi{}0.0010) is well outside the error bars for the value quoted in previous Monte Carlo simulations but in excellent agreement with more recent Monte Carlo renormalization-group results. The values of the critical and tricritical exponents, with the exception of the leading thermal tricritical exponent, are in excellent agreement with previous calculations, conjectured values, and Monte Carlo renormalization-group studies.