Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Log inSign up
Challenges
Datasets
Workspaces
Papers
Discussions
Leaderboard
Blog
Job Board
Q3AS

© 2026 Aqora Quantum S.A.S.

TermsPrivacyLegal Notice

Journal of Physical Studies

Properties of the phase transition in the transverse Ising model

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

Published Jan 1, 1998• 1 citation
Publisher

Abstract

The phase transition properties of the quantum spin{1/2 Ising model in a transverse magnetic eld are reconsidered with the help of the mean eld approximation, the Ginzburg criterion, and the renormalization group theory.A special attention is paid to the phase transitions whose properties are determined by variations of the external transverse eld and to the low{temperature phase transitions due to temperature variations.The classical{to{quantum crossover is investigated in details.A new crossover eect is established and discussed.

DOI
10.30970/jps.02.181

Related papers

The spin S Ising model with a transverse field

J. Oitmaa, G J Coombs

The authors have investigated the properties of the Ising model in a transverse field for general spin S by the method of high-temperature series. Analysis of the series yields the form of the phase diagram in the temperature field plane. The authors also investigate the variation of critical field with spin, and present evidence for classical-quantum crossover at T=0 for all spin values.

Journal of Physics C Solid State Physics•Jan 20, 1981•25 citations

Quantum phase transitions in spin systems and the high temperature limit of continuum quantum eld theories

Subir Sachdev A

We study the nite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum eld theory. Particular attention is focussed on the high temperature limit of the continuum eld theory, the socalled \quantum-critical region. Basic features of crossovers are illustrated by a simple solvable model of dilute spinless fermions, and a partially solvable model of dilute bosons. The low frequency relaxational behavior of the quantum-critical region is displayed in the solution of the transverse-eld Ising model. The insights from these simple models lead to a fairly complete understanding of the system of primary interest: the two-dimensional quantum rotor model, whose phase transition is expected to be in the same universality class as those in antiferromagnetic Heisenberg spin models. Recent work on the experimental implications of these results for the cuprate compounds is briey reviewed.

•Aug 18, 1995•5 citations

Properties of the random-field Ising model in a transverse magnetic field

T. Senthil

We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension $d>2$, there is at low strength of randomness and transverse field a phase with true long-range order that is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite-temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e., the logarithm of the diverging time scale rises as a power of the diverging length scale.

arXiv:cond-mat/9709164•Physical review. B, Condensed matter•Apr 1, 1998•24 citations

Ising model with a transverse field in two dimensions: Phase diagram and critical properties from a real-space renormalization group

Zvi Friedman

Critical indices, the critical line, and the crossover scaling function for the free energy are calculated for the two-dimensional Ising model with a transverse field using a quantum-mechanical version of the real-space renormalization group. The critical behavior as function of the transverse field at a small finite temperature changes from that of a three-dimensional to that of a two-dimensional Ising behavior, as the critical line is approached.

Physical review. B, Condensed matter•Feb 1, 1978•24 citations

Quantum crossover in the transverse Ising model

Ian D. Lawrie

The critical behaviour of d dimensional Ising models in a transverse magnetic field, Gamma , is investigated using a quantal generalisation of the Landau-Ginzburg-Wilson free-energy functional introduced by Hertz and Young (1976). A variational approximation of the Hartree type allows a detailed analysis: behaviour near the critical line, Gamma = Gammac(T) is governed by the exponents of the d dimensional spherical model (which are mean-field-like for d>or=4). However, the point ( Gamma ,T)=( Gammac(0),0) is multicritical in nature, and characterised by the exponents of the (d+1) dimensional spherical model. Crossover scaling functions, valid near the multicritical point, are found for the longitudinal susceptibility and free energy. They involve the crossover exponent phiT; for 2<d<or=3 this is equal to the (d+1) dimensional correlation length exponent, nud+1=1/(d-1); for 3<d<or=4, we find phiT=1/2(4-d), while for d>4, no crossover occurs. These results are shown to be consistent, for all d>2, with the finite-size scaling analogy suggested by Suzuki (1976) and others.

Journal of Physics C Solid State Physics•Mar 28, 1978•38 citations

Quantum effects in the renormalization group approach to phase transitions

A. P. Young

The renormalization group approach to critical phenomena is developed for quantum mechanical problems with non-commuting operators. Applying the theory to the spin 1 / 2 Ising model with a transverse field Gamma it is found that the critical exponents are those of the Ising model with Gamma =0 if the transition occurs at T>0. However, for transitions at T=0 the critical behaviour of the d-dimensional transverse system corresponds to that of the (d+1)-dimensional Ising model with Gamma =0, in agreement with series expansion predictions. At T=0 the dynamic, as well as static, critical behaviour is given by mean field theory for d>3.

Journal of Physics C Solid State Physics•Aug 7, 1975•108 citations
The phase transition properties of the quantum spin{1/2 Ising model in a transverse magnetic eld are reconsidered with the help of the mean eld approximation, the Ginzburg criterion, and the renormalization group theory.A special attention is paid to the phase transitions whose properties are determined by variations of the external transverse eld and to the low{temperature phase transitions due to temperature variations.The classical{to{quantum crossover is investigated in details.A new crossover eect is established and discussed.
We study the nite temperature crossovers in the vicinity of a zero temperature quantum phase transition. The universal crossover functions are observables of a continuum quantum eld theory. Particular attention is focussed on the high temperature limit of the continuum eld theory, the socalled \quantum-critical region. Basic features of crossovers are illustrated by a simple solvable model of dilute spinless fermions, and a partially solvable model of dilute bosons. The low frequency relaxational behavior of the quantum-critical region is displayed in the solution of the transverse-eld Ising model. The insights from these simple models lead to a fairly complete understanding of the system of primary interest: the two-dimensional quantum rotor model, whose phase transition is expected to be in the same universality class as those in antiferromagnetic Heisenberg spin models. Recent work on the experimental implications of these results for the cuprate compounds is briey reviewed.
We consider the effect of a random longitudinal field on the Ising model in a transverse magnetic field. For spatial dimension d>2d>2d>2, there is at low strength of randomness and transverse field a phase with true long-range order that is destroyed at higher values of the randomness or transverse field. The properties of the quantum phase transition at zero temperature are controlled by a fixed point with no quantum fluctuations. This fixed point also controls the classical finite-temperature phase transition in this model. Many critical properties of the quantum transition are therefore identical to those of the classical transition. In particular, we argue that the dynamical scaling is activated, i.e., the logarithm of the diverging time scale rises as a power of the diverging length scale.
The critical behaviour of d dimensional Ising models in a transverse magnetic field, Gamma , is investigated using a quantal generalisation of the Landau-Ginzburg-Wilson free-energy functional introduced by Hertz and Young (1976). A variational approximation of the Hartree type allows a detailed analysis: behaviour near the critical line, Gamma = Gammac(T) is governed by the exponents of the d dimensional spherical model (which are mean-field-like for d>or=4). However, the point ( Gamma ,T)=( Gammac(0),0) is multicritical in nature, and characterised by the exponents of the (d+1) dimensional spherical model. Crossover scaling functions, valid near the multicritical point, are found for the longitudinal susceptibility and free energy. They involve the crossover exponent phiT; for 2<d<or=3 this is equal to the (d+1) dimensional correlation length exponent, nud+1=1/(d-1); for 3<d<or=4, we find phiT=1/2(4-d), while for d>4, no crossover occurs. These results are shown to be consistent, for all d>2, with the finite-size scaling analogy suggested by Suzuki (1976) and others.
The renormalization group approach to critical phenomena is developed for quantum mechanical problems with non-commuting operators. Applying the theory to the spin 1 / 2 Ising model with a transverse field Gamma it is found that the critical exponents are those of the Ising model with Gamma =0 if the transition occurs at T>0. However, for transitions at T=0 the critical behaviour of the d-dimensional transverse system corresponds to that of the (d+1)-dimensional Ising model with Gamma =0, in agreement with series expansion predictions. At T=0 the dynamic, as well as static, critical behaviour is given by mean field theory for d>3.