The phase transition in the one-dimensional Ising Model with 1/r2 interaction energy

@article{Frhlich1982ThePT,
  title={The phase transition in the one-dimensional Ising Model with 1/r2 interaction energy},
  author={J{\"u}rg Fr{\"o}hlich and Thomas J. Spencer},
  journal={Communications in Mathematical Physics},
  year={1982},
  volume={84},
  pages={87-101}
}
We prove the existence of a spontaneous magnetization at low temperature for the one-dimensional Ising Model with 1/r2 interaction energy. 
The one-dimensional long-range ferromagnetic Ising model with a periodic external field
We consider the one-dimensional ferromagnetic Ising model with very long-range interaction under a periodic, biased and weak external field and prove that at sufficiently low temperatures the modelExpand
GROUND STATES OF ONE-DIMENSIONAL LONG-RANGE FERROMAGNETIC ISING MODEL WITH EXTERNAL FIELD
A zero-temperature phase-diagram of the one-dimensional ferromagnetic Ising model is investigated. It is shown that at zero temperature spins of any compact collection of lattice points withExpand
Phase transition for a one-dimensional lattice gas with hard core
Existence of a phase transition is proved for a one-dimensional lattice gas with long-range interaction and nearest neighbor exclusion.
Restoring long-range order in one-dimensional superconductivity by power-law hopping
1. We demonstrate that long-range superconducting order is restored for 1=2 < < c, with 5=4 < c < 3=2. This conclusion is supported by a DMRG analysis of the model.
A one-dimensional model exhibiting phase transition
A one-dimensional model with two spin variables having a unique ground state and at least two extreme limit Gibbs states is constructed.
The phase transition in the discrete Gaussian chain with 1/r2 interaction energy
We exhibit a phase transition from a rough high-temperature phase to a rigid (localized) low-temperature phase in the discrete Gaussian chain with 1/r2 interaction energy. This transition is relatedExpand
Study of a Long Range Perturbation of a One-Dimensional Kac Model
We consider a one dimensional ferromagnetic Ising spin system with interactions that correspond to a 1/r2 long range perturbation of the usual Kac model. We apply a coarse graining procedure widelyExpand
Phase diagram in the quantum XY model with long-range interactions
We study the d-dimensional quantum XY model with ferromagnetic long-range interaction decaying as r-p in terms of boson operators, by employing the coherent state path integral approach. We haveExpand
Bethe lattice approximation of the one-dimensional Potts model with long-range interaction
Abstract The mean-field approximation of the one-dimensional ferromagnetic p -state Potts model with interactions decaying as a power law is developed using a modified Bethe lattice recentlyExpand
The relationship between phase transitions and percolation in models with ground-state degeneracy
A criterion for the uniqueness of limiting Gibbs states in classical models with unique ground states is formulated. Various applications of this criterion formulated in the terminology ofExpand
...
1
2
3
4
5
...

References

SHOWING 1-10 OF 12 REFERENCES
Rigorous entropy-energy arguments
We present a method for making rigorous various arguments which predict that certain situations are unstable because of a balance of energy vs. entropy. As applications, we give yet another proofExpand
Correlations in Ising Ferromagnets. I
An inequality relating binary correlation functions for an Ising model with purely ferromagnetic interactions is derived by elementary arguments and used to show that such a ferromagnet cannotExpand
Statistical mechanics of a one-dimensional lattice gas
We study the statistical mechanics of an infinite one-dimensional classical lattice gas. Extending a result ofvan Hove we show that, for a large class of interactions, such a system has no phaseExpand
An Ising ferromagnet with discontinuous long-range order
An infinite one-dimensional Ising ferromagnetM with long-range interactions is constructed and proved to have the following properties. (1)M has an order-disorder phase transition at a finiteExpand
Non-existence of spontaneous magnetization in a one-dimensional Ising ferromagnet
AbstractIt is proved that an infinite linear chain of spins μj=±1, with an interaction energy $$H = - \Sigma J(i - j)\mu _i \mu _j $$ has zero spontaneous magnetization at all finite temperatures,Expand
The random walk representation of classical spin systems and correlation inequalities
Ferromagnetic lattice spin systems can be expressed as gases of random walks interacting via a soft core repulsion. By using a mixed spinrandom walk representation we present a unified approach toExpand
Correlation inequalities and the decay of correlations in ferromagnets
AbstractWe prove a variety of new correlation inequalities which bound intermediate distance correlations from below by long distance correlations. Typical is the following which holds for spin 1/2Expand
...
1
2
...