# On the Absence of Replica Symmetry Breaking and Decay of Correlations in the Random Field Ising Model

@article{Roldan2018OnTA, title={On the Absence of Replica Symmetry Breaking and Decay of Correlations in the Random Field Ising Model}, author={Jamer Roldan and Roberto Vila}, journal={arXiv: Mathematical Physics}, year={2018} }

This work is concerned with the theory of the Random Field Ising Model with presence of special non-Gaussian random fields on the hypercubic and hexagonal lattices. On the hypercubic lattice, we shown the absence of replica symmetry in any dimensions, at any temperature and field strength, almost surely. On the hexagonal lattice we obtained the decay ratio of the correlations.

No Paper Link Available

## References

SHOWING 1-10 OF 50 REFERENCES

### Replica Symmetry Breaking in the Random Field Ising Model

- Physics
- 1992

We discuss the critical behavior of the random field Ising model, using techniques of replica symmetry breaking familiar from the theory of spin glasses and random manifolds. Using an approximation…

### Absence of Replica Symmetry Breaking in the Random Field Ising Model

- Physics
- 2015

It is shown that replica symmetry is not broken in the random field Ising model in any dimension, at any temperature and field strength, except possibly at a measure-zero set of exceptional…

### On the Decay of Correlations in the Random Field Ising Model

- Mathematics
- 2017

In a celebrated 1990 paper, Aizenman and Wehr proved that the two-dimensional random field Ising model has a unique infinite volume Gibbs state at any temperature. The proof is ergodic-theoretic in…

### Some properties of random Ising models

- Mathematics, Physics
- 1985

We consider an Ising model with random magnetic fieldhi and random nearest-neighbor couplingsJij. The random variableshi andJij are independent and identically distributed with a nice enough…

### A Note on Exponential Decay in the Random Field Ising Model

- PhysicsJournal of Statistical Physics
- 2018

For the two-dimensional random field Ising model (RFIM) with bimodal (i.e., two-valued) external field, we prove exponential decay of correlations either (i) when the temperature is larger than the…

### The ground state of the three-dimensional random-field Ising model

- Physics
- 1985

We prove that the three-dimensional Ising model in a random magnetic field exhibits long-range order at zero temperature and small disorder. Hence the lower critical dimension for this model is two…

### Hysteresis in random-field Ising model on a Bethe lattice with a mixed coordination number

- Physics
- 2016

We study zero-temperature hysteresis in the random-field Ising model on a Bethe lattice where a fraction c of the sites have coordination number z = 4 while the remaining fraction 1 − c have z = 3.…

### Phase transition in the 3d random field Ising model

- Physics
- 1988

We show that the three-dimensional Ising model coupled to a small random magnetic field is ordered at low temperatures. This means that the lower critical dimension,dl for the theory isdl≦2, settling…

### General properties of overlap probability distributions in disordered spin systems. Towards Parisi ultrametricity

- Psychology
- 1998

For a very general class of probability distributions in disordered Ising spin systems, in the thermodynamical limit, we prove the following property for overlaps among real replicas. Consider the…

### Rounding of first-order phase transitions in systems with quenched disorder.

- PhysicsPhysical review letters
- 1989

For random-field models, this work rigorously proves uniqueness of the Gibbs state 2D Ising systems, and absence of continuous symmetry breaking in the Heisenberg model in d\ensuremath{\le}4, as predicted by Imry and Ma.