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arXiv:2212.01278 · Physical review. B./Physical review. B

Thermal first-order phase transitions, Ising critical points, and reentrance in the Ising-Heisenberg model on the diamond-decorated square lattice in a magnetic field

Jozef Strečka, Katarína Karľová, Taras Verkholyak, Nils Caci, Stefan Weßel, A. Honecker

Published Apr 4, 2023• 10 citations
arXivHTMLPDF

Abstract

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.

DOI
10.1103/physrevb.107.134402

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arXiv:0909.4191•physica status solidi (b)•Dec 22, 2009•23 citations
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.
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice exhibits an intriguing temperature-driven phase transition in a magnetic field between a classical ferrimagnetic phase and a quantum monomer-dimer phase. A generalized decoration-iteration transformation accurately maps the considered model to an effective spin-1/2 Ising model on a square lattice with temperature-dependent effective interactions and field, whereby the effective field vanishes at the phase boundary separating the classical ferrimagnetic phase from the quantum monomer-dimer phase. Typical features of the magnetization, magnetic susceptibility and specific heat in the vicinity of discontinuous and continuous thermal phase transitions between the classical ferrimagnetic phase and the quantum monomer-dimer phase are elucidated.
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.
The spin-1/2 Heisenberg antiferromagnet on the frustrated diamond-decorated square lattice is known to feature various zero-field ground-state phases, consisting of extended monomer-dimer and dimer-tetramer ground states as well as a ferrimagnetic regime. Using a combination of analytical arguments, density matrix renormalization group (DMRG), exact diagonalization as well as sign-problem-free quantum Monte Carlo (QMC) calculations, we investigate the properties of this system and the related Lieb lattice in the presence of a finite magnetic field, addressing both the ground-state phase diagram as well as several thermodynamic properties. In addition to the zero-field ground states, we find at high magnetic field a spin-canted phase with a continuously rising magnetization for increasing magnetic field strength as well as the fully polarized paramagnetic phase. At intermediate field strength, we identify a first-order quantum phase transition line between the ferrimagnetic and the monomer-dimer regime. This first-order line extends to finite temperatures, terminating in a line of critical points that belong to the universality class of the two-dimensional Ising model.
The spin-1/2 Ising-Heisenberg model on the extended Lieb lattice in a magnetic field is exactly mapped onto an effective spin-1/2 Ising model on the square lattice. The ground-state phase diagram comprises the quantum antiferromagnetic (QAF), quantum monomer-dimer (MD), classical ferrimagnetic (FRI), and classical ferromagnetic phase. The MD-FRI ground-state phase boundary extends to finite temperatures as a dome-shaped surface of discontinuous thermal transitions bounded by a line of Ising critical points. The QAF phase is enclosed by a surface of continuous thermal transitions evolving from the QAF-MD and QAF-FRI ground-state phase boundaries. Monte Carlo simulations fully confirm the existence and nature of both continuous and discontinuous thermal phase transitions obtained by exact and approximate analytical calculations.
The spin-1/2 Ising-Heisenberg model on a diamond-decorated square lattice is exactly solved by the decoration-iteration transformation, which establishes an exact mapping correspondence with the spin-1/2 Ising model on a square lattice with an effective temperature-dependent interaction between the nearest-neighbor spins. Exact results for the pair correlation function and spontaneous magnetization of the Heisenberg spins gained from the exact mapping equivalence allow a straightforward implementation of the concurrence, which may serve as a measure of the bipartite entanglement within decorating Heisenberg spin pairs. It is evidenced that the concurrence gradually diminishes upon increase of temperature above a disordered monomer-dimer ground state until it completely vanishes at a threshold temperature, while the concurrence is either always zero above a spontaneously ordered ferrimagnetic ground state or it shows a peculiar thermally assisted reentrance accompanied with a mutual coexistence of the spontaneous ferrimagnetic long-range order and the thermal entanglement.
Ground-state and finite-temperature behaviour of the mixed spin-1/2 and spin-1 Ising–Heisenberg model on decorated planar lattices consisting of inter-connected diamonds is investigated by means of the generalised decoration–iteration mapping transformation. The obtained exact results clearly point out that this model has a rather complex ground state composed of two unusual quantum phases, which is valid regardless of the lattice topology as well as the spatial dimensionality of the investigated system. It is shown that the diamond-like decorated planar lattices with a sufficiently high coordination number may exhibit a striking critical behaviour including reentrant phase transitions with two or three consecutive critical points.