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 Physics A Mathematical and General

Metastable states near the phase boundary: a finite-lattice study

Chris J. Hamer

Published Apr 21, 1983• 5 citations
Publisher

Abstract

The energy of the metastable vacuum in a complex magnetic field has been computed for the Hamiltonian field theory version of the Ising model in (1+1)D, using finite-lattice methods. Evidence is found for an essential singularity at the phase boundary, as predicted by the droplet model.
DOI
10.1088/0305-4470/16/6/019

Related papers

First-order phase transition and metastability in the critical two-dimensional Ising model

S. B. Rutkevich

The fermionic version of the two-dimensional Ising model in a uniform magnetic field is studied. Its approximate but rather accurate solution was obtained recently in a variational procedure based on the BCS ansatz for the ground state. Here, this solution is continued analytically into the complex H-plane in the vicinity of the origin. In the ferromagnetic phase an essential singularity in the free-energy is observed at the point H=0 of the type predicted by the droplet condensation theory. Simple phenomenological estimates for the radius of the critical droplet and for the rate of decay of metastable states are confirmed by microscopic calculations.

Journal of Physics A Mathematical and General•Jun 21, 1995•3 citations

Metastability in the (1+1)D Ising model: a primitive droplet model calculation

C K Harris

Using a primitive droplet model in conjunction with recent exact results for the surface free energies of Ising droplets on a square lattice with anisotropic couplings, the author obtains an expression for the principal non-universal amplitude appearing in the imaginary part of the small field metastable state energy of the Hamiltonian field theory version of the Ising model in (1+1)D. The calculation is in very good numerical agreement with the results of a recent finite lattice study.

Journal of Physics A Mathematical and General•Jun 1, 1984•2 citations

Numerical transfer-matrix study of metastability in thed=2 Ising model

C. C. A. Günther, Per Arne Rikvold, M. A. Novotny

We apply a generalized transfer-matrix method to the d=2 Ising ferromagnet at H\ensuremath{\ne}0 and T${\mathit{T}}_{\mathit{c}}$ to obtain complex constrained free energies. Although the method does not explicitly introduce droplets, the imaginary parts of those constrained free energies that correspond to the metastable state are accurately predicted by a field-theoretical droplet model. The free energy of a critical droplet is given by an equilibrium Wulff construction, and we find evidence for Goldstone modes on its surface. These results indicate that our approach provides a nonperturbative numerical continuation of the free energy around the essential singularity at H=0.

arXiv:cond-mat/9308019•Physical Review Letters•Dec 13, 1993•35 citations

Decay of the metastable phase in d = 1 and d = 2 Ising models

S. B. Rutkevich

We calculate perturbatively the tunneling decay rate $\ensuremath{\Gamma}$ of the metastable phase in the quantum $d=1$ Ising model in a skew magnetic field near the coexistence line $0<{h}_{x}<1, {h}_{z}\ensuremath{\rightarrow}\ensuremath{-}0$ at $T=0.$ It is shown that $\ensuremath{\Gamma}$ oscillates in the magnetic field ${h}_{z}$ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic $d=2$ Ising model at $T<{T}_{c},$ we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We also find evidence for the discrete-lattice corrections in this metastable phase free energy.

arXiv:cond-mat/9904059•Physical review. B, Condensed matter•Dec 1, 1999•49 citations

Ising model phase boundary

George Allen Baker Jr., D Kim

A large number of derivatives of the free energy with respect to the magnetic field are computed for the two-dimensional spin- 1 / 2 Ising model along the phase boundary H=0, T<T c . This series is found to be divergent, and so the phase boundary is a line of analytic singularities. The same analysis in three dimensions leads to the same conclusion, with lower precision.

Journal of Physics A Mathematical and General•Apr 1, 1980•35 citations

Droplet singularity

Douglas B. Abraham, Paul J. Upton

By an exact calculation on the planar Ising model we show that for all subcritical temperatures, the bubble model predicts the correct average distribution of matter contributing to the pair-spin correlation function in the two-particle sector. This considerably substantiates the bubble model which is generalized to higher dimensions with an external field h and then used to show that the free energy has an essential singularity in h of Andreev-Fisher form at all points along the phase boundary. We argue that such a singularity would also occur in the Baxter model.

Physical Review Letters•Mar 15, 1993•17 citations
The fermionic version of the two-dimensional Ising model in a uniform magnetic field is studied. Its approximate but rather accurate solution was obtained recently in a variational procedure based on the BCS ansatz for the ground state. Here, this solution is continued analytically into the complex H-plane in the vicinity of the origin. In the ferromagnetic phase an essential singularity in the free-energy is observed at the point H=0 of the type predicted by the droplet condensation theory. Simple phenomenological estimates for the radius of the critical droplet and for the rate of decay of metastable states are confirmed by microscopic calculations.
We apply a generalized transfer-matrix method to the d=2 Ising ferromagnet at H\ensuremath{\ne}0 and TTc{\mathit{T}}_{\mathit{c}}Tc​ to obtain complex constrained free energies. Although the method does not explicitly introduce droplets, the imaginary parts of those constrained free energies that correspond to the metastable state are accurately predicted by a field-theoretical droplet model. The free energy of a critical droplet is given by an equilibrium Wulff construction, and we find evidence for Goldstone modes on its surface. These results indicate that our approach provides a nonperturbative numerical continuation of the free energy around the essential singularity at H=0.
We calculate perturbatively the tunneling decay rate $\ensuremath{\Gamma}$ of the metastable phase in the quantum d=1d=1d=1 Ising model in a skew magnetic field near the coexistence line $0<{h}_{x}<1, {h}_{z}\ensuremath{\rightarrow}\ensuremath{-}0$ at T=0.T=0.T=0. It is shown that $\ensuremath{\Gamma}$ oscillates in the magnetic field hz{h}_{z}hz​ due to discreteness of the excitation energy spectrum. After mapping of the obtained results onto the extreme anisotropic d=2d=2d=2 Ising model at T<Tc,T<{T}_{c},T<Tc​, we verify in the latter model the droplet theory predictions for the free energy analytically continued to the metastable phase. We also find evidence for the discrete-lattice corrections in this metastable phase free energy.
By an exact calculation on the planar Ising model we show that for all subcritical temperatures, the bubble model predicts the correct average distribution of matter contributing to the pair-spin correlation function in the two-particle sector. This considerably substantiates the bubble model which is generalized to higher dimensions with an external field h and then used to show that the free energy has an essential singularity in h of Andreev-Fisher form at all points along the phase boundary. We argue that such a singularity would also occur in the Baxter model.