Ising model

About: Ising model is a research topic. Over the lifetime, 25508 publications have been published within this topic receiving 555000 citations.

Anomalous dynamical phase in quantum spin chains with long-range interactions

Abstract: The existence or absence of nonanalytic cusps in the Loschmidt-echo return rate is traditionally employed to distinguish between a regular dynamical phase (regular cusps) and a trivial phase (no cusps) in quantum spin chains after a global quench. However, numerical evidence in a recent study (J. C. Halimeh and V. Zauner-Stauber, arXiv:1610.02019) suggests that instead of the trivial phase, a distinct anomalous dynamical phase characterized by a novel type of nonanalytic cusps occurs in the one-dimensional transverse-field Ising model when interactions are sufficiently long range. Using an analytic semiclassical approach and exact diagonalization, we show that this anomalous phase also arises in the fully connected case of infinite-range interactions, and we discuss its defining signature. Our results show that the transition from the regular to the anomalous dynamical phase coincides with ${\mathbb{Z}}_{2}$-symmetry breaking in the infinite-time limit, thereby showing a connection between two different concepts of dynamical criticality. Our work further expands the dynamical phase diagram of long-range interacting quantum spin chains, and can be tested experimentally in ion-trap setups and ultracold atoms in optical cavities, where interactions are inherently long range.

Interface free energy and transition temperature of the square-lattice Ising antiferromagnet at finite magnetic field

Abstract: We use a simple method to calculate interface properties of the square-lattice Ising antiferromagnet with nearest neighbour interaction. The method bypasses the more complicated bulk problem by taking into account only interface configurations of spins and allows the inclusion of a finite magnetic field. From this we derive two new results: 1) the interface free energy associated with the coexistence of the two antiferromagnetic phases at finite magnetic field, and 2) the transition temperature as a function of the magnetic field which determines the phase boundary.

Molecular simulation of phase coexistence: Finite-size effects and determination of critical parameters for two- and three-dimensional Lennard-Jones fluids

Abstract: The subject of this paper is the investigation of finite-size effects and the determination of critical parameters for a class of truncated Lennard-Jones potentials. Despite significant recent progress in our ability to model phase equilibria in multicomponent mixtures from direct molecular simulations, the accurate determination of critical parameters remains a difficult problem. Gibbs ensemble Monte Carlo simulations with systems of controlled linear system size are used to obtain the phase behavior in the near-critical region for two- and three dimensional Lennard-Jones fluids with reduced cutoff radii of 3, 3.5, and 5. For the two-dimensional systems, crossover of the effective exponent for the width of the coexistence curve from mean field (β = 1/2 in the immediate vicinity of the critical point to Ising-like (β= 1/8) farther away is observed. Critical parameters determined by fitting the data that follow Ising-like behavior are in good agreement with literature values obtained with finite-size scaling methods. For the three-dimensional systems, no crossover to mean field-type behavior was apparent. Extrapolated results for the critical parameters are consistent with literature estimates for similar fluids. For both two- and three-dimensional fluids, system size effects on the coexistence curves away from the critical point are small, normally within simulation statistical uncertainties.

Introduction to the Dicke model: from equilibrium to nonequilibrium, and vice versa

Abstract: The Dicke model describes the coupling between a quantized cavity field and a large ensemble of two-level atoms. When the number of atoms tends to infinity, this model can undergo a transition to a superradiant phase, belonging to the mean-field Ising universality class. The superradiant transition was first predicted for atoms in thermal equilibrium and was recently realized with a quantum simulator made of atoms in an optical cavity, subject to both dissipation and driving. In this Progress Report, we offer an introduction to some theoretical concepts relevant to the Dicke model, reviewing the critical properties of the superradiant phase transition, and the distinction between equilibrium and nonequilibrium conditions. In addition, we explain the fundamental difference between the superradiant phase transition and the more common lasing transition. Our report mostly focuses on the steady states of atoms in single-mode optical cavities, but we also mention some aspects of real-time dynamics, as well as other quantum simulators, including superconducting qubits, trapped ions, and using spin-orbit coupling for cold atoms. These realizations differ in regard to whether they describe equilibrium or non-equilibrium systems.

Scaling theory of the random-field Ising model

Abstract: The scaling laws derived by Grinstein (1976) for the random-field Ising model (RFIM) are rederived on the assumption that the transition is second order and that the critical behaviour is controlled by a zero-temperature fixed point The scaling laws involve three independent exponents nu , eta and gamma , the last appearing in a modified hyperscaling relation, 2- alpha =(d-y) nu It is argued that such hyperscaling modifications are a general feature of phase transitions controlled by zero-temperature fixed points Explicit evaluation of the RFIM exponents in d=2+ epsilon dimensions, yields, to order epsilon , 1/ nu = epsilon , eta =1- epsilon /2 and y=1+ epsilon /2 The exponent nu is different from that of the pure model in (d-y) dimensions implying that no exact 'dimensional reduction' is possible near two dimensions