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Journal of Statistical Mechanics Theory and Experiment

Single-point ground states and residual entropies in the antiferromagnetic Ising model with multisite interaction on the tetrahedral chain: exact results

E. Jurčišinová, Marian Jurčisin

Published Jan 1, 2016• 2 citations
Publisher

Abstract

Abstract. The antiferromagnetic spin-1/2 Ising model with the presence of the multisite interaction and in the external magnetic field on the infinite tetrahedral chain is solved exactly by using the transfer matrix method. Using the exact expression for the free energy per site of the model the thermodynamic properties of the model are investigated in detail. It is shown that the total magnetisation per site forms the magnetisation plateaus at low temperatures, the properties of which depend on the strength of the multisite interaction. The set of all possible ground states is found and discussed. The existence of the so-called single-point ground states is shown and their properties are studied in detail. The entropy per site of the model is investigated and the exact expressions for the residual entropies of all ground states are found and their macroscopic degeneracies are discussed. The existence of the ground states with the same value of magnetisation but with different entropies is observed. In addition, the behaviour of the susceptibility and the specific heat is also studied.

DOI
10.1088/1742-5468/2016/01/013101

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The ground state and the thermodynamics of a spin-1/2 asymmetric diamond Ising--Heisenberg chain are considered. For the XYZXYZXYZ anisotropic Heisenberg interaction, the exact calculations of the free energy, entropy, heat capacity, magnetization, and magnetic susceptibility are performed using the method of decoration-iteration transformation. In the case of antiferromagnetic interactions (Ising and XXZXXZXXZ anisotropic Heisenberg ones), the ground state, magnetization process, temperature dependence of the magnetization, magnetic susceptibility, and heat capacity are investigated. The influence of geometric frustration and quantum fluctuations on these characteristics is studied.
In this paper the exact solution and correlation functions for a double-chain Ising model with multi-spin interactions and symmetric Hamiltonian density are obtained. The study employs the transfer matrix method to derive fundamental thermodynamic characteristics of the system. The main results include exact expressions for the partition function, free energy, internal energy, specific heat capacity, magnetization, susceptibility, and entropy in a strip of finite length and in the thermodynamic limit. The work provides explicit formulas for the eigenvalues and shows structure of eigenvectors of the transfer matrix. The expression for magnetization in the thermodynamic limit using components of normalized eigenvector corresponding to the maximum eigenvalue is obtained. A detailed analysis is conducted for a special case of interactions involving all kinds of two- and four-spin interactions. This gives the simplified formula for free energy, it is calculated using the root of quadratic equation. Using special relation between parameters the solution for gonihedric model on the plane is obtained. The research reveals properties of the system, including specific features of ground states and phase diagram characteristics. Particular attention is given to the behavior of physical quantities near frustration points and the investigation of spin correlation functions. Plots of physical characteristics, including inverse correlation length, illustrating the obtained results are constructed.