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

Communications in Theoretical Physics

Numerical Calculations for the Surface on a Semi-Infinite Ising Model with a Random Surface Field

Gang Sun, Jie Yang

Published Jan 30, 1995• 1 citation
Publisher

Abstract

We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.

DOI
10.1088/0253-6102/23/1/25

Related papers

Mean-field renormalization-group approaches to the surface on a semi-infinite Ising model with a random surface field

Gang Sun

We study the critical behavior of the surface on a semi-infinite simple-cubic-lattice Ising model with a bimodal random surface field by a large-cell mean-field renormalization-group method. Our results show that a surface ferromagnetic phase exists at weak random fields above the bulk critical temperature, and no signs of the tricritical point are found until the surface critical temperature decreases to that of the bulk.

Physical review. B, Condensed matter•Feb 1, 1995•1 citation

Monte Carlo study of surface critical phenomena: The special point

Martin Hasenbusch B

We study the special point in the phase diagram of a semi-infinite system where the bulk transition is in the three-dimensional Ising universality class. To this end we performed a finite-size-scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interaction. In order to check for the effect of leading bulk corrections we also simulated the spin-1/2 Ising model on the simple cubic lattice. We accurately estimated the surface enhancement coupling at the special point of these models. We find ${y}_{{t}_{1}}=0.718(2)$ and ${y}_{{h}_{1}}=1.6465(6)$ for the surface renormalization group exponents of the special transition. These results are compared with previous ones obtained by using field-theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore, we study the behavior of the surface transition near the special point, and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.

arXiv:1108.2425•Physical Review B•Oct 7, 2011•31 citations

Critical behavior of a semi-infinite Ising model with an edge

V. K. Saxena

A semi-infinite Ising model on a simple-cubic lattice, bounded by two perpendicular planes which meet at an edge, is studied with the Migdal-Kadanoff renormalization-group approach. It is found that the edge spins can order at a temperature higher than the bulk transition temperature if one of the surfaces is also ordered, whereas no edge ordering is possible if none of the surfaces nor the bulk are ordered. A complete phase diagram is presented in the parameter space of the model considered. Correlation-length critical exponents \ensuremath{\nu} and the crossover exponent \ensuremath{\varphi} are calculated and various universality classes are established.

Physical review. B, Condensed matter•Mar 1, 1987•5 citations

Renormalization-group approach to the Ising model with a free surface

Theodore W. Burkhardt, Erich Eisenriegler

We use simple position-space renormalization-group procedures involving only nearest-neighbor interactions to discuss the critical behavior of the ferromagnetically coupled semi-infinite Ising model with a free surface in two and three dimensions. In three dimensions for suitably enhanced surface couplings there are surface transitions and simultaneous surface-bulk transitions as well as the bulk transition. A phase diagram, critical exponents for the various transitions, and some representative magnetization profiles are calculated. Despite their simplicity, the renormalization transformations exhibit complete sets of fixed points for describing the various phase transitions and yield phase diagrams which are a significant improvement over mean-field theory. However, the calculated magnetization profiles show some unphysical features due to the finite cluster size on which the transformations are based.

Physical review. B, Solid state•Oct 1, 1977•124 citations

Surface magnetisation of the Ising ferromagnet in a semi-infinite cubic lattice: renormalisation group approach

Anna Chame, Constantino Tsallis

Using a recently introduced renormalisation group method, the authors study the behaviour of the spontaneous surface and bulk magnetisations as functions of the temperature for an Ising ferromagnet in a semi-infinite cubic lattice for various J S /J B ratios (J S and J B respectively are the surface and bulk coupling constants). In particular, they study the extraordinary transition where the surface maintains its magnetisation as the bulk disorders: the authors find a discontinuity in the first derivative of the surface magnetisation at the bulk transition temperature. The criticality of the system (universality classes, critical exponents and amplitudes) is discussed as well.

Journal of Physics Condensed Matter•Dec 18, 1989•13 citations

STUDY OF SURFACE MAGNETISM IN A SEMI-INFINITE ISING FERROMAGNETIC SYSTEM

JIANG QIN, Zhenya Li, 苏州大学物理系

We use the mean field renormalization group method to treat the semi-infinite Ising ferromagnetic system with the amorphization of the surface. The critical behavior of the surface with a surface random field, including critical temperature, the possibility of tricritical and reentrant phenomena, are investigated in detail.

Acta Physica Sinica•Jan 1, 1989•1 citation
We study the critical behavior of the surface on a semi-infinite simple cubic lattice Ising model with a bimodal random surface field by large cell mean-field renormalization group method and Monte Carlo simulations. Our results show that the surface ferromagnetic phase exists in the weak random field range above the bulk critical temperature. The surface specific heat is not divergence and the susceptibility show a cusp singularity at the surface ferromagnetic-paramagnetic transition for a relatively large random field.
We study the special point in the phase diagram of a semi-infinite system where the bulk transition is in the three-dimensional Ising universality class. To this end we performed a finite-size-scaling study of the improved Blume-Capel model on the simple cubic lattice with two different types of surface interaction. In order to check for the effect of leading bulk corrections we also simulated the spin-1/2 Ising model on the simple cubic lattice. We accurately estimated the surface enhancement coupling at the special point of these models. We find yt1=0.718(2){y}_{{t}_{1}}=0.718(2)yt1​​=0.718(2) and yh1=1.6465(6){y}_{{h}_{1}}=1.6465(6)yh1​​=1.6465(6) for the surface renormalization group exponents of the special transition. These results are compared with previous ones obtained by using field-theoretic methods and Monte Carlo simulations of the spin-1/2 Ising model. Furthermore, we study the behavior of the surface transition near the special point, and finally we discuss films with special boundary conditions at one surface and fixed ones at the other.
A semi-infinite Ising model on a simple-cubic lattice, bounded by two perpendicular planes which meet at an edge, is studied with the Migdal-Kadanoff renormalization-group approach. It is found that the edge spins can order at a temperature higher than the bulk transition temperature if one of the surfaces is also ordered, whereas no edge ordering is possible if none of the surfaces nor the bulk are ordered. A complete phase diagram is presented in the parameter space of the model considered. Correlation-length critical exponents \ensuremath{\nu} and the crossover exponent \ensuremath{\varphi} are calculated and various universality classes are established.
We use simple position-space renormalization-group procedures involving only nearest-neighbor interactions to discuss the critical behavior of the ferromagnetically coupled semi-infinite Ising model with a free surface in two and three dimensions. In three dimensions for suitably enhanced surface couplings there are surface transitions and simultaneous surface-bulk transitions as well as the bulk transition. A phase diagram, critical exponents for the various transitions, and some representative magnetization profiles are calculated. Despite their simplicity, the renormalization transformations exhibit complete sets of fixed points for describing the various phase transitions and yield phase diagrams which are a significant improvement over mean-field theory. However, the calculated magnetization profiles show some unphysical features due to the finite cluster size on which the transformations are based.
Using a recently introduced renormalisation group method, the authors study the behaviour of the spontaneous surface and bulk magnetisations as functions of the temperature for an Ising ferromagnet in a semi-infinite cubic lattice for various J S /J B ratios (J S and J B respectively are the surface and bulk coupling constants). In particular, they study the extraordinary transition where the surface maintains its magnetisation as the bulk disorders: the authors find a discontinuity in the first derivative of the surface magnetisation at the bulk transition temperature. The criticality of the system (universality classes, critical exponents and amplitudes) is discussed as well.