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arXiv:1007.1873 · Acta Physica Polonica A

Rigorous Criterion for Reentrance in the Spin-1/2 Ising-Heisenberg Model on Diamond-Like Decorated Bethe Lattices

Jozef Strečka, Cesur Ekiz

Published Nov 1, 2010• 3 citations
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Abstract

The spin-1/2 Ising-Heisenberg model on diamond-like decorated Bethe lattices is exactly solved with the help of decoration-iteration transformation and exact recursion relations.It is shown that the model under investigation exhibits reentrant phase transitions whenever a sufficiently high coordination number of the underlying Bethe lattice is considered.

DOI
10.12693/aphyspola.118.725

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The spin-1/2 Ising-Heisenberg model on diamond-like decorated Bethe lattices is exactly solved with the help of decoration-iteration transformation and exact recursion relations.It is shown that the model under investigation exhibits reentrant phase transitions whenever a sufficiently high coordination number of the underlying Bethe lattice is considered.
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The spin-1/2 Ising-Heisenberg model on diamond-like decorated Bethe lattices is exactly solved in the presence of the longitudinal magnetic field by combining the decoration-iteration mapping transformation with the method of exact recursion relations.In particular, the ground state and low-temperature magnetization process of the ferrimagnetic version of the considered model is investigated in detail.Three different magnetization scenarios with up to two consecutive fractional magnetization plateaus were found, whereas the intermediate magnetization plateau may either correspond to the classical ferrimagnetic spin arrangement and/or the field-induced quantum ferrimagnetic spin ordering without any classical counterpart.
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.