# Relaxation at finite temperature in fully frustrated Ising models

@article{Walter2011RelaxationAF, title={Relaxation at finite temperature in fully frustrated Ising models}, author={Jean-Charles Walter and Christophe Chatelain}, journal={Journal of Statistical Mechanics: Theory and Experiment}, year={2011}, volume={2012}, pages={P02010} }

We consider by means of Monte Carlo simulations the relaxation in the paramagnetic phase of the anti-ferromagnetic Ising model on a triangular lattice and of a fully frustrated Ising model on a square lattice. In contrast to previous studies of the second model, we show that spin–spin correlation functions do not decay with a stretched-exponential law at low temperature but that both models display an exponential decay with logarithmic corrections that are interpreted as the signature of…

## 2 Citations

### Binary lattice-gases of particles with soft exclusion: exact phase diagrams for tree-like lattices

- Materials Science
- 2021

We study equilibrium properties of binary lattice-gases comprising A and B particles, which undergo continuous exchanges with their respective reservoirs, maintained at chemical potentials μ A = μ B…

### Modeling the formation and positioning of intracellular macromolecular assemblies: Application to bacterial DNA segregation

- Biology, Physics
- 2020

This HDR defense will offer a physical perspective of intracellular phase transition with the example of bacterial DNA segregation, and the motion of ribosomes along messenger RNA, an example of unidimensional inhomogeneous transport giving rise to different dynamical regimes.

## References

SHOWING 1-10 OF 21 REFERENCES

### Logarithmic corrections in the ageing of the fully frustrated Ising model

- Physics
- 2007

We study the dynamics of the critical two-dimensional fully frustrated Ising model by means of Monte Carlo simulations. The dynamical exponent is estimated at equilibrium and is shown to be…

### Monte Carlo study of a compressible Ising antiferromagnet on a triangular lattice.

- PhysicsPhysical review. B, Condensed matter
- 1996

It is found that the coupling to the strain removes the frustration of the rigid model and the simulations show a transition from the disordered to an ordered, striped phase at low temperatures.

### Zero-temperature phase transitions of an antiferromagnetic Ising model of general spin on a triangular lattice

- Physics
- 1997

We map the ground-state ensemble of antiferromagnetic Ising model of spin-S on a triangular lattice to an interface model whose entropic fluctuations are proposed to be described by an effective…

### Elastic antiferromagnets on a triangular lattice

- Physics
- 1986

Elastic Ising antiferromagnets are studied on a triangular lattice. Magnetic 'frustration' is removed at low temperatures by a lattice distortion, and the resulting ground state has alternating rows…

### Percolation transition and the onset of nonexponential relaxation in fully frustrated models

- Physics
- 1999

We numerically study the dynamical properties of fully frustrated models in two and three dimensions. The results obtained support the hypothesis that the percolation transition of the…

### Nonequilibrium critical dynamics of the triangular antiferromagnetic Ising model.

- PhysicsPhysical review. E, Statistical, nonlinear, and soft matter physics
- 2003

This work investigates the nonequilibrium critical dynamics of antiferromagnetic Ising model on a two-dimensional triangular lattice via dynamic Monte Carlo simulation employing spin-flip kinetics and exhibits an interesting initial-state dependence.

### Precursor phenomena in frustrated systems.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

It is suggested that precursor phenomena in frustrated systems are due either to disorder and/or to frustration, giving a consistent interpretation also for the limiting cases of Ising spin glass and of ising fully frustrated model, where also the Potts transition is vanishing.

### Geometric frustration in buckled colloidal monolayers

- PhysicsNature
- 2008

Experiment and theory reveal single-particle dynamics governed by in-plane lattice distortions that partially relieve frustration and produce ground states with zigzagging stripes and subextensive entropy, rather than the more random configurations and extensive entropy of the antiferromagnetic Ising model.

### Vortex dynamics and entropic forces in antiferromagnets and antiferromagnetic Potts models.

- PhysicsPhysical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics
- 1999

This work examines the Potts model in detail, shows explicitly how this force is felt through local fields, and calculates the defects' mobility, and takes two approaches to measuring this force numerically.

### Ground-state correlations and universality in two-dimensional fully frustrated systems

- Physics
- 1980

The spin-spin correlation function in the ground state of some two-dimensional fully frustrated spin models are investigated. The correlations are long ranged and decay as…