Random Surface Field Research Articles

A Monte Carlo study of random surface field effect on layering transitions

The effect of a random surface field, within the bimodal distribution, on the layering transitions in a spin- 1 2 Ising thin film is investigated using Monte Carlo simulations. It is found that the layering transitions depend strongly on the concentration p of the disorder of the surface magnetic field, for a fixed temperature, surface and external magnetic fields. Indeed, the critical concentration p c ( k ) at which the magnetisation of each layer k changes the sign discontinuously, decreases with increase in applied surface magnetic field, for fixed values of the temperature T and the external magnetic field H. Moreover, the behaviour of the layer magnetisations as well as the distribution of positive and negative spins in each layer, are also established for specific values of H s , H, p and temperature T.

Logarithmic corrections in the two-dimensional Ising model in a random surface field

In the two-dimensional Ising model weak random surface field is predicted to be a marginally irrelevant perturbation at the critical point. We study this question by extensive Monte Carlo simulations for various strength of disorder. The calculated effective (temperature or size dependent) critical exponents fit with the field-theoretical results and can be interpreted in terms of the predicted logarithmic corrections to the pure system's critical behaviour.

Phase Diagrams of the Semi-Infinite Spin-1/2 Ising Model and Spin-1/2 Ising Film in a Random Transverse Surface Field

The critical behavior of both semi-infinite spin-1/2 Ising system and spin-1/2 Ising film in a random transverse surface field has been studied within an effective field theory. The effect of the ratio R of the surface exchange interaction to the bulk one, random transverse surface field and film thickness on the phase diagrams are investigated.

Phase Diagrams of the Semi-Infinite Spin-1/2 Ising Model and Spin-1/2 Ising Film in a Random Transverse Surface Field

Phase Diagrams of the Semi-Infinite Spin-1/2 Ising Model and Spin-1/2 Ising Film in a Random Transverse Surface Field

Surface magnetism in the semi-infinite Heisenberg ferromagnet

Surface phase diagrams of a semi-infinite simple cubic anisotropic Heisenberg ferromagnet with spin- 1 2 in the presence of a random surface field are examined by use of the effective-field theory within the frame of Ising-Heisenberg two-particle cluster approximation. Surface phase diagrams are obtained and the surface tricritical behavior is found for a large value of the surface exchange coupling J s .

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

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

Numerical Calculations for the Surface on a Semi-Infinite Ising Model with a Random Surface Field11The project supported by National Natural Science Foundation of China and the Chinese Academy of Sciences through Grant LWTZ-1298

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.

Surface phase diagrams of the spin-1 Ising model with a random surface field

Surface phase diagrams are investigated by means of the mean-field renormalization group method for Ising systems of spin-1 and spin- 1 2 ferromagnets with spin-1 surface layers. The tricritical point and reentrant phase transition of the surface magnetism are found.

Phase diagram of a trimodal random surface field.

We determine the phase diagram of a semi-infinite simple-cubic-lattice Ising model when a diluted random field is taken on the surface. We show, within effective-field theory, that surface tricritical behavior can be determined as a function of the field dilution. For a given critical value of the field dilution, the tricritical behavior disappears, whatever the values of surface exchange are.

Ising Model of Thin Film with Random Surface Field

Ising Model of Thin Film with Random Surface Field

Critical behaviour near multiple junctions and dirty surfaces in the two-dimensional Ising model

We consider m two-dimensional semi-infinite planes of Ising spins joined together through surface spins and study the critical behaviour near to the junction. The m=0 limit of the model - according to the replica trick - corresponds to the semi-infinite Ising model in the presence of a random surface field (RSFI). Using conformal mapping, second-order perturbation expansion around the weakly- and strongly-coupled planes limits and differential renormalization group, we show that the surface critical behaviour of the RSFI model is described by Ising critical exponents with logarithmic corrections to scaling, while at multiple junctions (m>2) the transition is first order. There is a spontaneous junction magnetization at the bulk critical point.

Critical behavior at dirty surfaces

The influence of quenched surface disorder — i.e. quenched disorder that is located at the bounding surface of a macroscopic system — on the surface critical behavior of such systems is investigated. To this end a class of semi-infinite continuum models of then-vector type with random surface interactions is studied. Both the case of surface transitions at a bulk critical point as well as that of surface transitions at a bulk tricritical point is considered. General irrelevance/relevance criteria of the Harris type are derived for both short-range and long-range correlated random surface interactions. These are used to assess the stability of the pure system critical behavior and to point out when random surface field or enhancement disorder is expected to be relevant.

Surface magnetism in a random surface field

Surface phase diagrams of a semi-infinite simple cubic spin 12 Ising system in a random surface field are investigated by the use of effective-field theory with correlations. Surface tricritical behavior is found, when the enhanced surface exchange interaction takes a large value.

Universality of surface critical behavior of the three-dimensional Ising model in a random surface field.

The Harris criterion is generalized to determine the relevance at bulk criticality (in the scaling theory sense) of a random ordering field acting at a surface only. For surface critical behavior of the three-dimensional Ising model the criterion predicts the random field to be irrelevant for the ordinary transition, and relevant for the surface-bulk multicritical point. Monte Carlo results for the ordinary transition verify the prediction. Moreover, surface critical behavior near substrates chemically altered in part, as used in a series of experiments by Franck and co-workers, is in the universality class mentioned above, and the value of ${\ensuremath{\beta}}_{1}$ found in a random surface experiment [D. J. Durian, and C. Franck, Phys. Rev. Lett. 59, 555 (1987)] agrees with the scaling prediction.