Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

arXiv:1707.05665 · Physical review. E

Interface tension in the improved Blume-Capel model

Martin Hasenbusch B

Published Sep 25, 2017• 0 citations
arXivHTMLPDF

Abstract

We study interfaces with periodic boundary conditions in the low-temperature phase of the improved Blume-Capel model on the simple cubic lattice. The interface free energy is defined by the difference of the free energy of a system with antiperiodic boundary conditions in one of the directions and that of a system with periodic boundary conditions in all directions. It is obtained by integration of differences of the corresponding internal energies over the inverse temperature. These differences can be computed efficiently by using a variance reduced estimator that is based on the exchange cluster algorithm. The interface tension is obtained from the interface free energy by using predictions based on effective interface models. By using our numerical results for the interface tension σ and the correlation length ξ obtained in previous work, we determine the universal amplitude ratios R_{2nd,+}=σ_{0}f_{2nd,+}^{2}=0.3863(6), R_{2nd,-}=σ_{0}f_{2nd,-}^{2}=0.1028(1), and R_{exp,-}=σ_{0}f_{exp,-}^{2}=0.1077(3). Our results are consistent with those obtained previously for the three-dimensional Ising model, confirming the universality hypothesis.

DOI
10.1103/physreve.96.032803

Related papers

Direct Monte Carlo Measurement of the Surface Tension in Ising Models

Martin Hasenbusch B, Fachbereich Physik, Universität Kaiserslautern +1 more

I present a cluster Monte Carlo algorithm that gives direct access to the interface free energy of Ising models. The basic idea is to simulate an ensemble that consists of both configurations with periodic and with antiperiodic boundary conditions. A cluster algorithm is provided that efficently updates this joint ensemble. The interface tension is obtained from the ratio of configurations with periodic and antiperiodic boundary conditions, respectively. The method is tested for the 3-dimensional Ising model. 1 1

•Jan 1, 1993•17 citations

Numerical transfer-matrix study of surface-tension anisotropy in Ising models on square and cubic lattices

Howard L. Richards, M. A. Novotny, Per Arne Rikvold

We compute by numerical transfer-matrix methods the surface free energy \ensuremath{\tau}(T), the surface stiffness coefficient \ensuremath{\kappa}(T), and the step free energy s(T) for Ising ferromagnets with (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L) square-lattice and (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}M) cubic-lattice geometries, into which an interface is introduced by imposing antiperiodic or plus/minus boundary conditions in one transverse direction. These quantities occur in expansions of the angle-dependent surface tension for either rough or smooth interfaces. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating \ensuremath{\tau}(T), \ensuremath{\kappa}(T), and s(T). The resulting transfer-matrix estimates are fully consistent with previous series and Monte Carlo studies, although current computational technology does not permit transfer-matrix studies of sufficiently large systems to show quantitative improvement over the previous estimates.

arXiv:cond-mat/9305010•Physical review. B, Condensed matter•Nov 15, 1993•13 citations

Universal amplitude ratios in the three-dimensional Ising universality class

Martin Hasenbusch B

We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain ${A}_{+}/{A}_{\ensuremath{-}}=0.536(2)$ and ${C}_{+}/{C}_{\ensuremath{-}}=4.713(7)$, where ${A}_{\ifmmode\pm\else\textpm\fi{}}$ and ${C}_{\ifmmode\pm\else\textpm\fi{}}$ are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts $+$ and $\ensuremath{-}$ indicate the high- and the low-temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high- and low-temperature series expansions, field theoretic methods, and experiments.

arXiv:1004.4983•Physical Review B•Nov 23, 2010•46 citations

1 New Estimates On Various Critical/Universal Quantities of the 3D Ising Model ∗

Martin Hasenbusch B, K. Pinn, Universität Münster

We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi**3, where fs is the singular part of the free energy.

•Jan 1, 1997•1 citation

Direct Monte Carlo measurement of the surface tension in Ising models

Martin Hasenbusch

I present a cluster Monte Carlo algorithm that gives direct access to the interface free energy of Ising models. The basic idea is to simulate an ensemble that consists of both configurations with periodic and with antiperiodic boundary conditions. A cluster algorithm is provided that efficently updates this joint ensemble. The interface tension is obtained from the ratio of configurations with periodic and antiperiodic boundary conditions, respectively. The method is tested for the 3-dimensional Ising model.

arXiv:hep-lat/9209016•Journal de Physique I•Mar 1, 1993•25 citations

Capillary Waves in Binder's Approach to the Interface Tension

U.‐J. Wiese

In Binder's approach the reduced interface tension sigma of the Ising model in the broken phase is determined from the finite volume effects of the partition function Z(M) at fixed total magnetization M. For small |M| the partition function of a system of size L^d with periodic boundary conditions is dominated by configurations with two interfaces, such that Z(M) ~ exp(- 2 sigma L^{d-1}). Capillary wave fluctuations of the interfaces correct this result to Z(M) ~ exp(- 2 sigma L^{d-1}) with x = -1. The knowledge of the pre-exponential behavior allows an improved fit of numerical data, and a determination of the interface stiffness.

arXiv:hep-lat/9209006•Sep 3, 1992•2 citations
We study interfaces with periodic boundary conditions in the low-temperature phase of the improved Blume-Capel model on the simple cubic lattice. The interface free energy is defined by the difference of the free energy of a system with antiperiodic boundary conditions in one of the directions and that of a system with periodic boundary conditions in all directions. It is obtained by integration of differences of the corresponding internal energies over the inverse temperature. These differences can be computed efficiently by using a variance reduced estimator that is based on the exchange cluster algorithm. The interface tension is obtained from the interface free energy by using predictions based on effective interface models. By using our numerical results for the interface tension σ and the correlation length ξ obtained in previous work, we determine the universal amplitude ratios R_{2nd,+}=σ_{0}f_{2nd,+}^{2}=0.3863(6), R_{2nd,-}=σ_{0}f_{2nd,-}^{2}=0.1028(1), and R_{exp,-}=σ_{0}f_{exp,-}^{2}=0.1077(3). Our results are consistent with those obtained previously for the three-dimensional Ising model, confirming the universality hypothesis.
I present a cluster Monte Carlo algorithm that gives direct access to the interface free energy of Ising models. The basic idea is to simulate an ensemble that consists of both configurations with periodic and with antiperiodic boundary conditions. A cluster algorithm is provided that efficently updates this joint ensemble. The interface tension is obtained from the ratio of configurations with periodic and antiperiodic boundary conditions, respectively. The method is tested for the 3-dimensional Ising model. 1 1
We compute by numerical transfer-matrix methods the surface free energy \ensuremath{\tau}(T), the surface stiffness coefficient \ensuremath{\kappa}(T), and the step free energy s(T) for Ising ferromagnets with (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L) square-lattice and (\ensuremath{\infty}\ifmmode\times\else\texttimes\fi{}L\ifmmode\times\else\texttimes\fi{}M) cubic-lattice geometries, into which an interface is introduced by imposing antiperiodic or plus/minus boundary conditions in one transverse direction. These quantities occur in expansions of the angle-dependent surface tension for either rough or smooth interfaces. The finite-size scaling behavior of the interfacial correlation length provides the means of investigating \ensuremath{\tau}(T), \ensuremath{\kappa}(T), and s(T). The resulting transfer-matrix estimates are fully consistent with previous series and Monte Carlo studies, although current computational technology does not permit transfer-matrix studies of sufficiently large systems to show quantitative improvement over the previous estimates.
We compute a number of universal amplitude ratios in the three-dimensional Ising universality class. To this end, we perform Monte Carlo simulations of the improved Blume-Capel model on the simple cubic lattice. For example, we obtain ${A}_{+}/{A}_{\ensuremath{-}}=0.536(2)$ and ${C}_{+}/{C}_{\ensuremath{-}}=4.713(7)$, where ${A}_{\ifmmode\pm\else\textpm\fi{}}$ and ${C}_{\ifmmode\pm\else\textpm\fi{}}$ are the amplitudes of the specific heat and the magnetic susceptibility, respectively. The subscripts +++ and $\ensuremath{-}$ indicate the high- and the low-temperature phase, respectively. We compare our results with those obtained from previous Monte Carlo simulations, high- and low-temperature series expansions, field theoretic methods, and experiments.
We present estimates for the 3D Ising model on the cubic lattice, both regarding interface and bulk properties. We have results for the interface tension, in particular the amplitude sigma0 in the critical law sigma = sigma0*t**mu, and for the universal combination R_ = sigma*xi**2. Concerning the bulk properties, we estimate the specific heat universal amplitude ratio A+/A_, together with the exponent alpha, the nonsingular background of energy and specific heat at criticality, together with the exponent nu. There are also results for the universal combination fs*xi**3, where fs is the singular part of the free energy.
I present a cluster Monte Carlo algorithm that gives direct access to the interface free energy of Ising models. The basic idea is to simulate an ensemble that consists of both configurations with periodic and with antiperiodic boundary conditions. A cluster algorithm is provided that efficently updates this joint ensemble. The interface tension is obtained from the ratio of configurations with periodic and antiperiodic boundary conditions, respectively. The method is tested for the 3-dimensional Ising model.
In Binder's approach the reduced interface tension sigma of the Ising model in the broken phase is determined from the finite volume effects of the partition function Z(M) at fixed total magnetization M. For small |M| the partition function of a system of size L^d with periodic boundary conditions is dominated by configurations with two interfaces, such that Z(M) ~ exp(- 2 sigma L^{d-1}). Capillary wave fluctuations of the interfaces correct this result to Z(M) ~ exp(- 2 sigma L^{d-1}) with x = -1. The knowledge of the pre-exponential behavior allows an improved fit of numerical data, and a determination of the interface stiffness.