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Publication# Thermal Ising Transition in the Spin-1/2 J(1)-J(2) Heisenberg Model

Abstract

Using an SU(2) invariant finite-temperature tensor network algorithm, we provide strong numerical evidence in favor of an Ising transition in the collinear phase of the spin-1/2 J(1)-J(2) Heisenberg model on the square lattice. In units of J(2), the critical temperature reaches a maximal value of T-c/J(2 )similar or equal to 0.18 around J(2)/J(1) similar or equal to 1.0. It is strongly suppressed upon approaching the zero-temperature boundary of the collinear phase J(2)/J(1 )similar or equal to 0.6, and it vanishes as 1/log(J(2)/J(1)) in the large J(2)/J(1) limit, as predicted by Chandra et al., [Phys. Rev. Lett. 64, 88 (1990)]. Enforcing the SU(2) symmetry is crucial to avoid the artifact of finite-temperature SU(2) symmetry breaking of U(1) algorithms, opening new perspectives in the investigation of the thermal properties of quantum Heisenberg antiferromagnets.

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Related concepts (26)

Ising model

The Ising model (ˈiːzɪŋ) (or Lenz-Ising model or Ising-Lenz model), named after the physicists Ernst Ising and Wilhelm Lenz, is a mathematical model of ferromagnetism in statistical mechanics. The model consists of discrete variables that represent magnetic dipole moments of atomic "spins" that can be in one of two states (+1 or −1). The spins are arranged in a graph, usually a lattice (where the local structure repeats periodically in all directions), allowing each spin to interact with its neighbors.

Phase transition

In chemistry, thermodynamics, and other related fields, a phase transition (or phase change) is the physical process of transition between one state of a medium and another. Commonly the term is used to refer to changes among the basic states of matter: solid, liquid, and gas, and in rare cases, plasma. A phase of a thermodynamic system and the states of matter have uniform physical properties. During a phase transition of a given medium, certain properties of the medium change as a result of the change of external conditions, such as temperature or pressure.

Critical exponent

Critical exponents describe the behavior of physical quantities near continuous phase transitions. It is believed, though not proven, that they are universal, i.e. they do not depend on the details of the physical system, but only on some of its general features. For instance, for ferromagnetic systems, the critical exponents depend only on: the dimension of the system the range of the interaction the spin dimension These properties of critical exponents are supported by experimental data.

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