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

Physical review. B, Condensed matter

Interface delocalization in the three-dimensional Ising model with a defect plane

A. Benyoussef, Abdallah El Kenz

Published Feb 1, 1993• 3 citations
Publisher

Abstract

Using mean-field theory, the finite-cluster approximation, and the real-space renormalization group, we study the spin-1/2 Ising model on a cubic lattice with a defect plane that divides the system into two semi-infinite ones. The phase diagrams, which represent the connection between defect-plane order and wetting phenomena, are given in the case of two equivalent semi-infinite systems (the same coupling) and in the case of different semi-infinite systems. These phase diagrams are in agreement with those conjectured qualitatively by Igloi and Indekeu.

DOI
10.1103/physrevb.47.2619

Related papers

Phase Diagram of the Semi-Infinite Ising Model in a Random Field

A.S. de Arruda, W. Figueiredo

We determine the phase diagram of the semi-infinite Ising model in a cubic lattice with a trimodal distribution of random fields on the surface. We use the mean-field renormalization group with the smallest possible clusters to show that a very small dilution of the random field at surface is sufficient to destroy the tricritical behavior.

Modern Physics Letters B•Sep 20, 1997•12 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

Criticality of the bond-diluted Ising ferromagnet in a semi-infinite simple-cubic lattice

L. R. da Silva, Constantino Tsallis, Enaldo F. Sarmento

We study the phase diagram and universality classes of the quenched bond-diluted spin-(1/2 Ising ferromagnet in a semi-infinite simple-cubic lattice with a (001) free surface. The approach (herein formulated for arbitrary values of the number of states q of the Potts model) is a real-space renormalization group which preserves two-spin correlation functions and uses clusters which have already proved to be very appropriate for the present structure. We observe that surface ferromagnetism persists below the two-dimensional (2D) percolation threshold ${p}_{c}^{2\mathrm{D}=(1/2}$, in fact down to ${p}_{c}$\ensuremath{\simeq}0.42. In addition to that we check that a conjectural extension of the Kasteleyn-Fortuin theorem is satisfied in the present particular case.

Physical review. B, Condensed matter•May 1, 1988•4 citations

Surface phase diagrams of a semi-infinite system with spin-1/2 bulk and spin-1 surface

A. Ezzaime, N. Hachem, El Mostafa Tari +2 more

Abstract The Migdal–Kadanoff renormalization group technique is applied to study a three-dimensional semi-infinite Ising system consisting of spin-1/2 sites in the bulk and spin-1 sites at the surface. According to the competition ratio between bulk and surface exchange interactions ( R = J B / J S ), two types of surface phase diagrams have been identified in the (surface crystal field, temperature) plane. These diagrams exhibit a rich variety of phase transition phenomena: surface, ordinary, extraordinary, and special second-order transitions, first-order transitions at the surface, as well as tricritical and multicritical points. Additionally, we list in a table the fixed points that govern the observed phases and phase transitions.

Physica Scripta•Jul 14, 2026•0 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

Critical wetting transitions in two-dimensional systems subject to long-ranged boundary fields

A. Drzewiński, Anna Maciołek, Artur Barasiński +1 more

Using the quasiexact density-matrix renormalization-group method and ground-state analysis we study interface delocalization transitions in wide two-dimensional Ising strips subject to long-ranged boundary fields with opposite signs at the two surfaces. Based on this approach, our explicit calculations demonstrate that critical wetting transitions do exist for semi-infinite two-dimensional systems even if the corresponding effective interface potentials decay asymptotically for large l as slow as l(-delta) with delta<2, where l is the distance of the mean interface position from the one-dimensional surface. This supersedes opposite claims by Kroll and Lipowsky [Phys. Rev. B 28, 5273 (1983)] and by Privman and Svrakić [Phys. Rev. B 37, 5974 (1988)] obtained within effective interface models. The corresponding wetting phase diagram is determined, including the cases delta=2 and delta=49 with the latter mimicking short-ranged surface fields. Our analysis highlights the limits of reliability of effective interface models.

Physical Review E•Apr 28, 2009•5 citations
Using mean-field theory, the finite-cluster approximation, and the real-space renormalization group, we study the spin-1/2 Ising model on a cubic lattice with a defect plane that divides the system into two semi-infinite ones. The phase diagrams, which represent the connection between defect-plane order and wetting phenomena, are given in the case of two equivalent semi-infinite systems (the same coupling) and in the case of different semi-infinite systems. These phase diagrams are in agreement with those conjectured qualitatively by Igloi and Indekeu.
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 study the phase diagram and universality classes of the quenched bond-diluted spin-(1/2 Ising ferromagnet in a semi-infinite simple-cubic lattice with a (001) free surface. The approach (herein formulated for arbitrary values of the number of states q of the Potts model) is a real-space renormalization group which preserves two-spin correlation functions and uses clusters which have already proved to be very appropriate for the present structure. We observe that surface ferromagnetism persists below the two-dimensional (2D) percolation threshold pc2D=(1/2{p}_{c}^{2\mathrm{D}=(1/2}pc2D=(1/2​, in fact down to pc{p}_{c}pc​\ensuremath{\simeq}0.42. In addition to that we check that a conjectural extension of the Kasteleyn-Fortuin theorem is satisfied in the present particular case.
Abstract The Migdal–Kadanoff renormalization group technique is applied to study a three-dimensional semi-infinite Ising system consisting of spin-1/2 sites in the bulk and spin-1 sites at the surface. According to the competition ratio between bulk and surface exchange interactions ( R = J B / J S ), two types of surface phase diagrams have been identified in the (surface crystal field, temperature) plane. These diagrams exhibit a rich variety of phase transition phenomena: surface, ordinary, extraordinary, and special second-order transitions, first-order transitions at the surface, as well as tricritical and multicritical points. Additionally, we list in a table the fixed points that govern the observed phases and phase transitions.
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 the quasiexact density-matrix renormalization-group method and ground-state analysis we study interface delocalization transitions in wide two-dimensional Ising strips subject to long-ranged boundary fields with opposite signs at the two surfaces. Based on this approach, our explicit calculations demonstrate that critical wetting transitions do exist for semi-infinite two-dimensional systems even if the corresponding effective interface potentials decay asymptotically for large l as slow as l(-delta) with delta<2, where l is the distance of the mean interface position from the one-dimensional surface. This supersedes opposite claims by Kroll and Lipowsky [Phys. Rev. B 28, 5273 (1983)] and by Privman and Svrakić [Phys. Rev. B 37, 5974 (1988)] obtained within effective interface models. The corresponding wetting phase diagram is determined, including the cases delta=2 and delta=49 with the latter mimicking short-ranged surface fields. Our analysis highlights the limits of reliability of effective interface models.