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physica status solidi (b)

Short‐range ±J interaction Ising spin glass in a transverse field on a Bethe lattice: a quantum‐spherical approach

T. K. Kopeć, Klaus D. Usadel

Published Dec 8, 2005• 10 citations
Publisher

Abstract

Abstract We consider the short‐range interaction disordered quantum Ising model with symmetric binary ±J bond distribution on the Bethe lattice (with coordination number z). The system exhibits quantum phase transition separating the spin glass and disordered phases where the quantum effect are regulated by a param‐ eter Δ describing the transverse field. By introducing a mapping of the quantum Hamiltonian of the model onto a soft‐spin action we consider it truncated version in a form of the solvable quantized spherical model. Quantum dynamics is examined via various correlation functions on the infinite tree which are evaluated in a closed form. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

DOI
10.1002/pssb.200541282

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Abstract We consider the short‐range interaction disordered quantum Ising model with symmetric binary ±J bond distribution on the Bethe lattice (with coordination number z). The system exhibits quantum phase transition separating the spin glass and disordered phases where the quantum effect are regulated by a param‐ eter Δ describing the transverse field. By introducing a mapping of the quantum Hamiltonian of the model onto a soft‐spin action we consider it truncated version in a form of the solvable quantized spherical model. Quantum dynamics is examined via various correlation functions on the infinite tree which are evaluated in a closed form. (© 2006 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
We consider the short-range-interaction disordered quantum spherical model with a symmetrical binary -bond distribution on the Bethe lattice (with coordination number z ). The system exhibits a quantum phase transition separating the spin-glass and disordered phases, where the quantum effects are regulated by a parameter describing the kinetic energy. The model admits, in the spherical limit, an exact solution both in the spin-glass phase and in the disordered phase. The quantum dynamics is examined via various correlation functions on the infinite tree, which are evaluated in closed form. A closed-form solution for the averaged free energy has been obtained, and various thermodynamic functions are explicitly derived in the form of low-temperature expansions.
We present an exact analytic solution of the short-range interaction disordered quantum spherical model with symmetric binary $\ifmmode\pm\else\textpm\fi{}J$ bond distribution on the Bethe lattice (with coordination number zzz). We find the zero temperature quantum spin glass phase transition for coordinations $z\ensuremath{\ge}3$ but not for the one-dimensional system (z=2)(z\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}2)(z=2). Quantum dynamics is examined via various correlation functions on the infinite tree which are evaluated in a closed form. The relationship between the results for a fully connected lattice $(z\ensuremath{\rightarrow}\ensuremath{\infty})$ and the usual mean-field approach is established.
We study the competition between bond randomness and quantum fluctuation in the infinite-range Ising model in the transverse field \ensuremath{\Delta} relevant for a number of pseudospin and magnetic quantum spin-glass systems. By introducing a mapping of the quantum Hamiltonian of the model onto a soft-spin action we consider it truncated version in a form of the solvable quantized spherical model. The resulting critical phase boundary Tcrit{\mathrm{T}}_{\mathrm{crit}}Tcrit​(\ensuremath{\Delta}) is in considerable agreement with the numerical estimates based on the Trotter-Suzuki and Monte Carlo methods. The equation of state for the system is also given.
We consider quantum rotors or Ising spins in a transverse field on a d-dimensional lattice, with random, frustrating, short-range, exchange interactions. The quantum dynamics are associated with a finite moment of inertia for the rotors, and with the transverse field for the Ising spins. For a suitable distribution of exchange constants, these models display spin-glass and quantum paramagnet phases and a zero-temperature (T) quantum transition between them. An earlier exact solution for the critical properties of a model with infinite-range interactions cna be reproduced by minimization of a Landau effective-action functional for the model in finite d with short-range interactions. The functional is expressed in terms of a composite spin field which is bilocal in time. The mean-field phase diagram near the T=0 critical point is mapped out as a function of T, strength of the quantum coupling, and applied fields. The spin-glass phase has replica symmetry breaking; but, as in the classical Ising spin glass, the order parameter becomes replica symmetric as T\ensuremath{\rightarrow}0. Next we examine the consequences of fluctuations about the mean field for the critical properties. Above d=8, and with certain restrictions on the values of the Landau couplings, we find that the transition is controlled by a Gaussian fixed point with mean-field critical exponents. For couplings not attracted by the Gaussian fixed point above d=8, and for all physical couplings below d=8, we find runaway renormalization-group flows to strong coupling. General scaling relations that should be valid even at the strong-coupling fixed point are proposed and compared with Monte Carlo simulations.
Abstract A spin‐½ XX chain with three‐spin and uniform long‐range interactions among the z components of the spins is constructed. Based upon the model, using the Jordan–Wigner transformation, the thermodynamic quantities and spin transports of the system are evaluated exactly. The phase diagram together with the key parameters characterizing quantum phase transitions is presented. It is noted that, similarly to classical first‐order phase transitions, there are also the metastable states “supercooled” and “superheated” in the first‐order quantum phase transitions. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)
The classical transverse field Ising spin-glass model with short-range interactions is investigated beyond the mean-field approximation for a real d -dimensional lattice. We use an appropriate non-trivial modification of the Bethe-Peierls method recently formulated for the Ising spin-glass. The zero-temperature critical value of the transverse field and the linear susceptibility in the paramagnetic phase are obtained analytically as functions of dimensionality d . The phase diagram is also calculated numerically for different values of d . In the limit , known mean-field results are consistently reproduced.