# Phase Transitions in Long-range Spin Models: The Power of Generalized Ensembles

@inproceedings{Reynal2005PhaseTI, title={Phase Transitions in Long-range Spin Models: The Power of Generalized Ensembles}, author={S. Reynal}, year={2005} }

This thesis uses generalized ensembles Monte Carlo methods to explore the critical behavior of spin chains with algebraically decaying interactions. The first part of this thesis investigates the phase diagram of a long-range Potts chain using a multicanonical algorithm. A new method based on spinodal points is proposed to detect the order of phase transitions. The boundary between first- and second-order transitions is located with unprecedented accuracy using this method, and a new, unusual… Expand

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#### References

SHOWING 1-10 OF 387 REFERENCES

Monte Carlo tests of renormalization-group predictions for critical phenomena in Ising models

- Physics
- 2001

Abstract A critical review is given of status and perspectives of Monte Carlo simulations that address bulk and interfacial phase transitions of ferromagnetic Ising models. First, some basic… Expand

Phase transitions in the quantum Ising and rotor models with a long-range interaction

- Physics
- 2001

We investigate the zero-temperature and finite-temperature phase transitions of quantum Ising and quantum rotor models. We here assume a long-range (falling off as 1/r d+σ , where r is the distance… Expand

Numerical studies of the Ising chain with long-range ferromagnetic interactions

- Physics
- 1970

A long-range Ising chain, which has ferromagnetic 1/r3 type interactions, has been studied by exact numerical calculation of thermodynamic properties of the sequence of systems of N spins (N<or=30).… Expand

Magnetic phase diagram of an alternating Ising chain with long-range interactions

- Physics
- 2001

The phase diagram of a two-sited magnetic Ising chain, with a long-range interaction in the form of ${1/r}^{1+\ensuremath{\sigma}},$ is studied. In this investigation, the finite-range scaling… Expand

Novel phase transition in two-dimensional xy-models with long-range interaction

- Physics
- 2005

The purpose of this article is to give an overview of results concerning ordering and critical properties of two-dimensional ferromagnets including the dipolar interaction. We investigate a… Expand

A long-range ferromagnetic spin model with periodic boundary conditions

- Physics
- 2002

A possible way to study long-range interacting particles in nite-innite periodic systems is applied to a modied Ising model with ferromagnetic interaction that decays as a 1=r law. We verify, by… Expand

Boundary between long-range and short-range critical behavior in systems with algebraic interactions.

- Physics, Medicine
- Physical review letters
- 2002

It is found that the boundary with short-range critical behavior occurs for interactions depending on distance r as r(-15/4), which answers a long-standing controversy between mutually conflicting renormalization-group analyses. Expand

Monte Carlo investigations of phase transitions: status and perspectives

- Physics, Mathematics
- 1999

Using the concept of finite-size scaling, Monte Carlo calculations of various models have become a very useful tool for the study of critical phenomena, with the system linear dimension as a… Expand

Cluster Monte Carlo algorithms for diluted spin glasses

- Physics
- 2004

Recently a cluster Monte Carlo algorithm has been used very successfully in the two-dimensional Edwards-Anderson (EA) model. We show that this algorithm and a variant thereof can also be used… Expand

Thermodynamics with long-range interactions: from Ising models to black holes.

- Physics, Medicine
- Physical review. E, Statistical, nonlinear, and soft matter physics
- 2003

Methods are presented which enables one to analyze the thermodynamics of systems with long-range interactions and it is found that a system interacting with a heat reservoir is in a probability distribution of canonical ensembles. Expand