Decay of the metastable phase in<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>1</mml:mn><mml:mn /></mml:math>and<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mml:mi>d</mml:mi><mml:mo>=</mml:mo><mml:mn>2</mml:mn><mml:mn /></mml:math>Ising models

Rutkevich, S. B.

doi:10.1103/physrevb.60.14525

Cited by 33 publications

(29 citation statements)

References 21 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This value differs from that obtained for the two dimensional critical Ising model [15,16] by the numerical factor π 2 /9 ≈ 1.0966. We suppose that this small discrepancy is the result of approximations used in [15,16], and the prefactor value A = η/(2π) is universal.…”

Section: Discussioncontrasting

confidence: 78%

The classical nucleation rate in two dimensions

Münster

Rutkevich

2003

Eur. Phys. J. C

View full text Add to dashboard Cite

In many systems in condensed matter physics and quantum field theory, first order phase transitions are initiated by the nucleation of bubbles of the stable phase. In homogeneous nucleation theory the nucleation rate Γ can be written in the form of the Arrhenius law: Γ = Ae −Hc . Here H c is the energy of the critical bubble, and the prefactor A can be expressed in terms of the determinant of the operator of fluctuations near the critical bubble state. In general it is not possible to find explicit expressions for A and H c . If the difference η between the energies of the stable and metastable vacua is small, the constant A can be determined within the leading approximation in η, which is an extension of the "thin wall approximation". We have done this calculation for the case of a model with a real-valued order parameter in two dimensions.

show abstract

Section: Discussioncontrasting

confidence: 78%

The classical nucleation rate in two dimensions

Münster

Rutkevich

2003

Eur. Phys. J. C

View full text Add to dashboard Cite

show abstract

“…When a (even very small) longitudinal field is introduced, an effective attractive potential is generated and the domain walls get confined in bound states whose nature is very similar to the mesons of QCD. Following the pioneering work by McCoy and Wu, confinement has then been found and investigated with various analytical and numerical methods in thermal equilibrium in several quantum one-dimensional models [3][4][5][6][7][8][9][10][11][12][13][14].…”

Section: Introductionmentioning

confidence: 99%

Confinement in the spectrum of a Heisenberg–Ising spin ladder

Lagnese¹,

Surace²,

Kormos³

et al. 2020

J. Stat. Mech.

View full text Add to dashboard Cite

We consider the quantum quench dynamics of a Heisenberg-Ising spin ladder which is an archetypal model in which confinement of elementary excitations is triggered by internal interactions rather than an external field. We show that the confinement strongly affects the light cone structure of correlation functions providing signatures of the velocities of the mesons of the model. We also show that the meson masses can be measured from the real time analysis of the evolution of the order parameter.

show abstract

“…Ergodicity breaking (in a disorder-free setting) may also occur when imposing externals fields: Refs. [34][35][36][37][38][39][40][41][42] show that for the case of a transverse field quantum Ising model, where an additionally applied longitudinal field leads to the confinement of excitations. This inhibits propagation of quasi-particles and thus prevents relaxation towards an ergodic steady state.…”

mentioning

confidence: 99%

Emergent Bloch Oscillations in a Kinetically Constrained Rydberg Spin Lattice

2021

View full text Add to dashboard Cite

We explore the relaxation dynamics of elementary spin clusters in a kinetically constrained spin system. Inspired by experiments with Rydberg lattice gases, we focus on the situation in which an excited spin leads to a "facilitated" excitation of a neighboring spin. We show that even weak interactions that extend beyond nearest neighbors can have a dramatic impact on the relaxation behavior: they generate a linear potential, which under certain conditions leads to the onset of Bloch oscillations of spin clusters. These hinder the expansion of a cluster and more generally the relaxation of many-body states towards equilibrium. This shows that non-ergodic behavior in kinetically constrained systems may occur as a consequence of the interplay between reduced connectivity of many-body states and weak interparticle interactions. We furthermore show that the emergent Bloch oscillations identified here can be detected in experiment through measurements of the Rydberg atom density, and discuss how spin-orbit coupling between internal and external degrees of freedom of spin clusters can be used to control their relaxation behavior.

show abstract

Decay of the metastable phase ind=1andd=2Ising models

Cited by 33 publications

References 21 publications

The classical nucleation rate in two dimensions

The classical nucleation rate in two dimensions

Confinement in the spectrum of a Heisenberg–Ising spin ladder

Emergent Bloch Oscillations in a Kinetically Constrained Rydberg Spin Lattice

Contact Info

Product

Resources

About