Metastable states of a spin glass chain at 0 temperature
نویسندگان
چکیده
2014 We consider an Ising spin glass chain at 0 temperature. The moments of the total number of metastable states and the typical number of metastable states at a given magnetization are calculated. We find that for all magnetizations less than or equal to mmax = 0.446042... there is an exponentially large number of metastable states. For magnetizations larger than mmax, there are no metastable states. The remanent magnetization mrem is known to be 1/3 for single spin flip dynamics when one starts at time t = 0 with all the spins aligned. This shows that the remanent magnetization is not given by the metastable states of maximum magnetization. Our results are valid for a spin glass chain with an arbitrary symmetric and continuous distribution of nearest neighbour interactions. J. Physique 47 (1986) 959-965 JUIN 1986, Classification Physics Abstracts 05.20
منابع مشابه
Exactly Solvable Model of Inergodic Spin Glass
A mean-field model of Ising spin glass with the Hamiltonian being a sum of the infinite-range ferromagnetic and random antiferromagnetic interactions has been studied. It is shown that this model has phase transition in external magnetic field into inergodic spin glass phase with a number of metastable states. The thermodynamic properties of metastable states are studied at T = 0 and near the t...
متن کاملMechanism for the failure of the Edwards hypothesis in the Sherrington-Kirkpatrick spin glass
The dynamics of the Sherrington-Kirkpatrick model at T=0 starting from random spin configurations is considered. The metastable states reached by such dynamics are atypical of such states as a whole, in that the probability density of site energies, p , is small at =0. Since virtually all metastable states have a much larger p 0 , this behavior demonstrates a qualitative failure of the Edwards ...
متن کاملDynamics within metastable states in a mean-field spin glass
In this letter we present a dynamical study of the structure of metastable states (corresponding to TAP solutions) in a mean-field spin–glass model. After reviewing known results of the statical approach, we use dynamics: starting from an initial condition thermalized at a temperature between the statical and the dynamical transition temperatures, we are able to study the relaxational dynamics ...
متن کاملComplexity as the driving force for glassy transitions
The glass transition is considered within two toys models, a mean field spin glass and a directed polymer in a correlated random potential. In the spin glass model there occurs a dynamical transition, where the the system condenses in a state of lower entropy. The extensive entropy loss, called complexity or information entropy, is calculated by analysis of the metastable (TAP) states. This yie...
متن کاملTime Decay of the Remanent Magnetization in the ±j Spin Glass Model at T = 0 Typeset Using Revt E X 1
Using the zero-temperature Metropolis dynamics, the time decay of the remanent magnetization in the ±J Edward-Anderson spin glass model with a uniform random distribution of ferromagnetic and antiferromagnetic interactions has been investigated. Starting from the saturation, the magnetization per spin m reveals a slow decrease with time, which can be approximated by a power law: m(t) = m ∞ + t ...
متن کامل