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Exact Free Energy of Dilute p-spin Model.

Nicolas Macris
2008
Reports

Abstract

In this paper we evaluate the free energy of the dilute p-spin model at finite temperature. Franz et al gave the first step to rigourize the replica solution for the dilute p-spin model by proving that the solution given by the Parisi replica scheme is a lower bound for p even. In this paper we also show that the replica symmetric solution is a lower bound to the free energy of the dilute p-spin model for the case of p odd in some region of the temperature and $p$ -spin parameters.

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Nicolas Macris
2008
Reports

Abstract

Official source

Related concepts (21)

Helmholtz free energy

In thermodynamics, the Helmholtz free energy (or Helmholtz energy) is a thermodynamic potential that measures the useful work obtainable from a closed thermodynamic system at a constant temperature (isothermal). The change in the Helmholtz energy during a process is equal to the maximum amount of work that the system can perform in a thermodynamic process in which temperature is held constant. At constant temperature, the Helmholtz free energy is minimized at equilibrium.

Spin glass

In condensed matter physics, a spin glass is a magnetic state characterized by randomness, besides cooperative behavior in freezing of spins at a temperature called 'freezing temperature' Tf. In ferromagnetic solids, component atoms' magnetic spins all align in the same direction. Spin glass when contrasted with a ferromagnet is defined as "disordered" magnetic state in which spins are aligned randomly or without a regular pattern and the couplings too are random.

Gibbs free energy

In thermodynamics, the Gibbs free energy (or Gibbs energy as the recommended name; symbol ) is a thermodynamic potential that can be used to calculate the maximum amount of work, other than pressure-volume work, that may be performed by a thermodynamically closed system at constant temperature and pressure. It also provides a necessary condition for processes such as chemical reactions that may occur under these conditions. The Gibbs free energy is expressed as where p is pressure, T is the temperature, U is the internal energy, V is volume, H is the enthalpy, and S is the entropy.

Related publications (1)

Exact Free Energy of Dilute p-spin Model.

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