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Communications in Theoretical Physics

Magnetic Phase Transitions in Quantum Ising Model with Annealed Antiferromagnetic Bond Randomness

Zhu-Pei Shi, Ruibao Tao

Published Jun 1, 1990• 1 citation
Publisher

Abstract

The effect of annealed antiferromagnetic bond randomness on the phase transitions of the Quantum Ising Model (QIM) is studied by using mean-field renormalization group method. It is argued that bond randomness drastically alters multicritical phase diagram via transverse field. Multicritical points and coexistence region of ferromagnetic and antiferromagnetic case exist only at weak transverse field, and are entirely eliminated at strong transverse field. The coexistence region diminishes in reducing the fluctuation interaction. This physical picture demonstrates that the competition between transverse field and exchange interaction and fluctuation interaction via bond randomness play an important role in generating multiphase structure. Another consequence of competition is that tricritical points of first-second order phase transitions are not entirely eliminated by bond randomness in two-dimensional QIM.

DOI
10.1088/0253-6102/13/4/433

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The effect of annealed antiferromagnetic bond randomness on the phase transitions of the Quantum Ising Model (QIM) is studied by using mean-field renormalization group method. It is argued that bond randomness drastically alters multicritical phase diagram via transverse field. Multicritical points and coexistence region of ferromagnetic and antiferromagnetic case exist only at weak transverse field, and are entirely eliminated at strong transverse field. The coexistence region diminishes in reducing the fluctuation interaction. This physical picture demonstrates that the competition between transverse field and exchange interaction and fluctuation interaction via bond randomness play an important role in generating multiphase structure. Another consequence of competition is that tricritical points of first-second order phase transitions are not entirely eliminated by bond randomness in two-dimensional QIM.
In view of the recently seen dramatic effect of quenched random bonds on tricritical systems, we have conducted a renormalization-group study on the effect of quenched random magnetic fields on the tricritical phase diagram of the spin-1 Ising model in d=3d\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}3d=3. We find that random fields convert first-order phase transitions into second-order phase transitions more effectively than random bonds. The coexistence region is extremely flat, attesting to an unusually small tricritical exponent ${\ensuremath{\beta}}_{u}$. The random-field phase diagram is strikingly asymmetric. To accommodate this asymmetry, the second-order boundary exhibits reentrance.
It is argued on general grounds that bond randomness drastically alters multicritical phase diagrams via a random-field mechanism. For example, tricritical points and critical end points are entirely eliminated (d\ensuremath{\le}2) or depressed in temperature (d>2). These predictions are confirmed by a renormalization-group calculation. Another consequence of this phenomenon is that, under bond randomness, the phase transitions of q-state Potts models are second order for all q at dimensionality d\ensuremath{\le}2.
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.
The physics of quantum Ising model (qIm) plays an important role in quantum many body system. We study and present the results of qIm and longer range quantum Ising model (lqIm) in presence of strong correlation. We do the quantum field theoretical renormalization group (RG) calculation to study the behaviour of RG flow lines for different couplings for different region of parameter space. We show how the strong correlation effect enrich the quantum physics of these two systems. We show explicitly that the ordered ferromagnetic (FM) phase to the disorder quantum paramagnet (dqpI) quantum phase transition occurs for only in the strongly correlated regime for qIm and the dqpI phase appears for non-interacting and attractive regime. We show explicitly for lqIm that FM to dqpI transition occurs at the extremely correlated region and also the dqpI phase appears in correlated regime. We show that short range FM coupling and longer range coupling are competiting with each other and also the effect of strong correlation in this competition. We also show the most interesting feature that the transverse field oppose the FM coupling of qIm but it is favour the longer range coupling of lqIm. We find the evidence of another disorder quantum paramagnetic (dqpII) phase due to the relevance of longer range coupling. We also present the existence of another quantum phase transition from dqpII phase to FM phase. We show explicitly that there is no phase transition from dqpI phase to dqpII phase rather they coexists. This work provides a new perspective not only for the statistical physics of quantum Ising model but also for the quantum many body systems.
It is argued on general grounds that bond randomness drastically alters multicritical phase diagrams via a random-field mechanism. For example, tricritical points and critical endpoints are entirely eliminated (in spatial dimension d≤2) or depressed in temperature (d>2). These predictions are confirmed by a renormalization-group calculation.1 Another consequence of this phenomenon is that, under bond randomness, the phase transitions of q-state Potts models are second order for all q at dimensionality d≤2.
Quantum multicritical points (QMCPs) emerge at the junction of two or more quantum phase transitions due to the interplay of disparate fluctuations, leading to novel universality classes. While quantum critical points have been well characterized, our understanding of QMCPs is much more limited, even though they might be less elusive to study experimentally than quantum critical points. Here, we characterize the QMCP of an interacting heterogeneous quantum system in two and three dimensions, the ferromagnetic random transverse-field Ising model (RTIM). The QMCP of the RTIM emerges due to both geometric and quantum fluctuations, studied here numerically by the strong disorder renormalization group method. The QMCP of the RTIM is found to exhibit ultraslow, activated dynamic scaling, governed by an infinite disorder fixed point. This ensures that the obtained multicritical exponents tend to the exact values at large scales, while also being universal---i.e., independent of the form of disorder---providing a solid theoretical basis for future experiments.