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The European Physical Journal B

Order disorder transitions in Ising models in transverse fields with second neighbour interactions

Parongama Sen

Published Jun 1, 1995• 5 citations
Publisher
DOI
10.1007/bf01324531

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In the present work, we investigate the phase transitions of the Ising model with interactions between first (J1), second (J2) and third (J3) neighbours in the square lattice with transverse magnetic field. In this study, we adopt antiferromagnetic interactions between first and second neighbours and consider third-neighbours interactions to be both ferromagnetic and antiferromagnetic. The description of the classical and quantum phase transitions of the model is carried out by adopting the cluster mean-field approximation with four sites. As a result, we identified that strong enough third-neighbor interactions lead to the disappearance of tricriticality at the boundary between the superantiferromagnetic (SAF) and paramagnetic (PM) phases. In particular, tricriticality is more sensitive to the presence of ferromagnetic interactions, disappearing for |J3| ă 0.3|J1| in the absence of transverse field. In the presence of antiferromagnetic J3, we find first-order transitions between the degenerate staggered dimer phase and the PM phase. Furthermore, we find a change in the nature of the SAF-PM phase transitions introduced by quantum fluctuations. This phenomenon, called quantum annealed criticality (QAC), consists of classical first-order phase transitions that become second-order phase transitions in the presence of a strong enough transverse field. Our results allow establishing a range of parameters J2 and J3 for which it is possible to find QAC. The analysis of the model criticality allows concluding that a strong enough J3 interaction eliminates the QAC phenomenon. Therefore, our results suggest that attempts to realize QAC in a square lattice system should avoid strong interactions between third neighbors, mainly if these interactions are ferromagnetic.

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Recently, there has been interest in the problems of disorder in the Ising model in a transverse field, which may apply to DKDP-KDP mixed systems and diluted vanadates. The site and bond diluted transverse Ising models have already been studied using Green's function techniques along with the coherent potential approximation. However, the situation as regards to the existence of a second order phase transition and the divergence of the static susceptibility is not very clear. In the present paper, a spin ½ Ising model in a transverse field and random bond (site) dilution is studied by variational cluster and perturbation expansion method. The critical temperature for the existence of a second order phase transition is calculated as a function of concentration of bonds (spins) and the transverse field. Variation of the critical concentration, for the existence of phase transition, is studied as a function of the transverse field. A phase diagram in the temperature-concentration-transverse field space is constructed. The static susceptibility is calculated and is found to diverge at the critical temperature, as is expected for the existence of a second order phase transition.

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Properties of the phase transitions in the transverse Ising model

L. De Cesare, Ileana Rabuffo, Dimo I. Uzunov

•Jan 1, 1998•0 citations
In the present work, we investigate the phase transitions of the Ising model with interactions between first (J1), second (J2) and third (J3) neighbours in the square lattice with transverse magnetic field. In this study, we adopt antiferromagnetic interactions between first and second neighbours and consider third-neighbours interactions to be both ferromagnetic and antiferromagnetic. The description of the classical and quantum phase transitions of the model is carried out by adopting the cluster mean-field approximation with four sites. As a result, we identified that strong enough third-neighbor interactions lead to the disappearance of tricriticality at the boundary between the superantiferromagnetic (SAF) and paramagnetic (PM) phases. In particular, tricriticality is more sensitive to the presence of ferromagnetic interactions, disappearing for |J3| ă 0.3|J1| in the absence of transverse field. In the presence of antiferromagnetic J3, we find first-order transitions between the degenerate staggered dimer phase and the PM phase. Furthermore, we find a change in the nature of the SAF-PM phase transitions introduced by quantum fluctuations. This phenomenon, called quantum annealed criticality (QAC), consists of classical first-order phase transitions that become second-order phase transitions in the presence of a strong enough transverse field. Our results allow establishing a range of parameters J2 and J3 for which it is possible to find QAC. The analysis of the model criticality allows concluding that a strong enough J3 interaction eliminates the QAC phenomenon. Therefore, our results suggest that attempts to realize QAC in a square lattice system should avoid strong interactions between third neighbors, mainly if these interactions are ferromagnetic.
Abstract This paper focuses on the ground state phase diagram of a 1D spin‐1/2 quantum Ising model with competing first and second nearest neighbour interactions known as the axial next nearest neighbour Ising model in the presence of a transverse magnetic field. Here, using quantum correlations, both numerically and analytically, some evidence is provided to clarify the identification of the ground state phase diagram. Local quantum correlations play a crucial role in detecting the critical lines either revealed or hidden by symmetry‐breaking. A non‐symmetry‐breaking disorder transition line can be identified by the first derivative of both entanglement of formation and quantum discord between nearest neighbour spins. In addition, the quantum correlations between the second neighbour spins can also be used to reveal Kosterlitz–Thouless phase transition when their interaction strength grows and becomes closer to the first nearest neighbour one. The results obtained using the Jordan–Wigner transformation confirm the accuracy of the numerical case.
Recently, there has been interest in the problems of disorder in the Ising model in a transverse field, which may apply to DKDP-KDP mixed systems and diluted vanadates. The site and bond diluted transverse Ising models have already been studied using Green's function techniques along with the coherent potential approximation. However, the situation as regards to the existence of a second order phase transition and the divergence of the static susceptibility is not very clear. In the present paper, a spin ½ Ising model in a transverse field and random bond (site) dilution is studied by variational cluster and perturbation expansion method. The critical temperature for the existence of a second order phase transition is calculated as a function of concentration of bonds (spins) and the transverse field. Variation of the critical concentration, for the existence of phase transition, is studied as a function of the transverse field. A phase diagram in the temperature-concentration-transverse field space is constructed. The static susceptibility is calculated and is found to diverge at the critical temperature, as is expected for the existence of a second order phase transition.