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Physica Scripta

Reentrant phenomenon in the decorated ising model

Sheng Chen, Yanyi Wu, Junyi Lu, Baohua Teng

Published Nov 2, 2023• 2 citations
Publisher

Abstract

Abstract Based on the transverse-field Ising model, this paper utilizes the theory of correlated effective fields to explore the ferromagnetic phase transition properties of nanoislands with decorated lattice. The findings suggest that the unique phase transition properties of the system are predominantly determined by the surface atoms, while the transverse field and decorating exchange interaction impact the specific details of the phase transition properties. Additionally, the magnetization of each lattice follows a quantitative relationship, in which the magnetization of the decorated lattice is weaker and that of the central lattice is stronger.

DOI
10.1088/1402-4896/ad0933

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Abstract Based on the transverse-field Ising model, this paper utilizes the theory of correlated effective fields to explore the ferromagnetic phase transition properties of nanoislands with decorated lattice. The findings suggest that the unique phase transition properties of the system are predominantly determined by the surface atoms, while the transverse field and decorating exchange interaction impact the specific details of the phase transition properties. Additionally, the magnetization of each lattice follows a quantitative relationship, in which the magnetization of the decorated lattice is weaker and that of the central lattice is stronger.
The thermal phase transitions of a spin-1/2 Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field are investigated using a decoration-iteration transformation and classical Monte Carlo simulations. A generalized decoration-iteration transformation maps this model exactly onto an effective classical Ising model on the square lattice with temperature-dependent effective nearest-neighbor interactions and magnetic field strength. The effective field vanishes along a ground-state phase boundary of the original model, separating a ferrimagnetic and a quantum monomer-dimer phase. At finite temperatures this phase boundary gives rise to an exactly solvable surface of discontinuous (first-order) phase transitions, which terminates in a line of Ising critical points. The existence of discontinuous reentrant phase transitions within a narrow parameter regime is reported and explained in terms of the low-energy excitations from both phases. These exact results, obtained from the mapping to the zero-field effective Ising model, are corroborated by classical Monte Carlo simulations of the effective model.
Within the framework of an effective-field theory with correlation evaluated for the Ising model with transverse field, the authors discuss the following cases: a diluted ferromagnetic square lattice with a transverse field; the magnetic behaviour of a transverse Ising model with diluted surface in a simple cubic lattice; and the surface magnetism of random transverse field at the surface. The surface magnetism is examined as a function of Delta =(J s /J)-1, the concentrations p and q of magnetic atoms at the surface, and Omega s and Omega b , the surface and bulk transverse field respectively. The phase diagrams for surface ordering are obtained and some characteristic behaviours of magnetism at the diluted surface are presented. The present framework is quite superior to the standard MFA, and whenever comparison is possible a satisfactory qualitative (and to a certain extent quantitative) agreement with results available in the literature is found.
Abstract The static critical behavior of a 2D decorated ferromagnetic Ising model on a triangular lattice has been investigated by the methods of computational physics. For nodal spins, ferromagnetic exchange interaction between the first nearest neighbors and antiferromagnetic interaction between the next nearest neighbors have been taken into account. Exchange interaction Jd between nodal and decorated spins varies within [–3.0, 3.0]. For different values of Jd, the ground state of the model has been determined, critical temperatures have been calculated, and a phase diagram has been constructed. It has been shown that the magnitude of exchange interaction with decorated spins influences the type of phase transition to the paramagnetic state.
We investigate the ground-state and finite-temperature properties of a mixed spin-1/2 and spin-1 Ising model on a decorated square (Lieb) lattice incorporating a uniaxial single-ion anisotropy and magnetic field. By employing the generalized decoration-iteration transformation, the model is mapped exactly onto an effective spin-1/2 Ising model on the square lattice characterized by an effective nearest-neighbor interaction and an effective field. The studied model consequently becomes exactly solvable even for finite values of the applied magnetic field whenever the effective field vanishes. The ground-state analysis reveals three distinct phases: ferrimagnetic phase (FRI), disordered phase (DP), and ferromagnetic (FM) phase. The ground-state boundary between FRI and DP phases gives rise to a dome-shaped surface of discontinuous thermal phase transitions, which is terminated by a line of Ising-type critical points associated with continuous thermal phase transitions. Both continuous and discontinuous thermal phase transitions belong to the exactly solvable parameter regime defined by a vanishing effective field in spite of the fact that the applied magnetic field is finite. Two consecutive discontinuous thermally-induced reentrant phase transitions DP-FRI-DP are identified in a narrow parameter region. The exact analytical predictions including reentrance, field- and thermally-driven phase transitions are independently verified by classical Monte Carlo simulations.