The thermodynamic limit of the quenched free energy of magnetic systems with random interactions

1982 ◽  
Vol 15 (1) ◽  
pp. L51-L54 ◽  
Author(s):  
S GoulartRosa
Keyword(s):  
Free Energy ◽  
Thermodynamic Limit ◽  
Magnetic Systems ◽  
Random Interactions

METASTABLE STATES IN THE HOPFIELD MODEL

1990 ◽  
Vol 04 (01) ◽  
pp. 143-150 ◽  
Author(s):  
CLAUDIO PROCESI ◽  
BRUNELLO TIROZZI
Keyword(s):  
Free Energy ◽  
Finite Number ◽  
Thermodynamic Limit ◽  
Metastable States ◽  
Hopfield Model ◽  
Zero Temperature

We describe the properties of the free energy of the Hopfield model with a finite number of patterns and describe its dynamic at zero temperature in the space of overlaps in the thermodynamic limit.

3-D SPIN GLASSES AND ISING MODELS NEW METHODS ON NEW ARCHITECTURES

1993 ◽  
Vol 04 (01) ◽  
pp. 217-221
Author(s):  
GYAN BHANOT
Keyword(s):  
Phase Transition ◽  
Free Energy ◽  
Ising Model ◽  
Thermodynamic Limit ◽  
Spin Glasses ◽  
Weak Coupling ◽  
Ising Models ◽  
Parallel Architectures ◽  
Strong Indication ◽  
New Methods

I describe work on 3-d Spin Glasses and the 3-d Ising Model done in collaboration with Michael Creutz at BNL and Jan Lacki at IAS Princeton. We have developed novel techniques to study these systems that make use of parallel architectures. For 3-d spin glasses, our results give strong indication that there is no phase transition in the thermodynamic limit whereas for the Ising model, we are able to extend the weak coupling expansion of the average free energy to 50 excited bonds.

Chemical Tension in VLS Nanostructure Growth Process: From Nanohillocks to Nanowires

2007 ◽  
Vol 1017 ◽  
Author(s):  
Na Li ◽  
Teh Y. Tan ◽  
Ulrich Gösele
Keyword(s):  
Free Energy ◽  
Energy Release ◽  
Gibbs Free Energy ◽  
Thermodynamic Limit ◽  
Equilibrium Model ◽  
Growth Process ◽  
Energy State ◽  
Crystal Layer ◽  
Global Equilibrium ◽  
Minimum Gibbs Free Energy

AbstractABSTRACTWe formulate a global equilibrium model to describe the growth of 1-d nanostructures in the VLS process by including also the chemical tension in addition to the physical tensions. The chemical tension derives from the Gibbs free energy release due to the growth of a crystal layer. The system global equilibrium is attained via the balance of the static physical tensions and the dynamic chemical tension, which allows the system to reach the minimum Gibbs free energy state. The model predicts, and provides conditions for the growth of nanowires of all sizes exceeding a lower thermodynamic limit. The model also predicts the conditions distinguishing the growth of nanaohillocks from nanowires.

scholarly journals Landau effective Hamiltonian and its application to magnetic systems

2018 ◽  
Vol 26 (1) ◽  
pp. 19-28
Author(s):  
K. M. Haponenko ◽  
A. I. Sokolovsky
Keyword(s):  
Free Energy ◽  
Landau Theory ◽  
Microscopic Theory ◽  
Order Parameters ◽  
Effective Hamiltonian ◽  
Magnetic Systems ◽  
Nonequilibrium States ◽  
Ferromagnetic System ◽  
Definition Of ◽  
Phenomenological Landau Theory

The Landau definition of the effective Hamiltonian (of the nonequilibrium free energy) is realized in a microscopic theory. According to Landau remark, the consideration is based on classical statistical mechanics. In his approach nonequilibrium states coinciding with equilibrium fluctuations are taken into account (the Onsager principle). The definition leads to the exact fulfillment of the Boltzmann principle written in the form with the complete free energy. The considered system is assumed to consist of two subsystems. The first subsystem is an equilibrium one. The second subsystem is a nonequilibrium one and its state is described by quantities that are considered as order parameters. The effective Hamiltonian is calculated near equilibrium in the form of a series in powers of deviations of the order parameters from their equilibrium values. The coefficients of the series are expressed through equilibrium correlation functions of the order parameters. In the final approximation correlations of six and more order parameters are neglected and correlations of four parameters are assumed to be small that leads to the corresponding perturbation theory. The developed theory is compared with the phenomenological Landau theory of phase transitions of the second kind. The obtained results are concretized for paramagnetic-ferromagnetic system. The consideration is restricted by paramagnetic phase.

scholarly journals Quantum Hopfield Model

Physics ◽  
2020 ◽  
Vol 2 (2) ◽  
pp. 184-196 ◽  
Author(s):  
Masha Shcherbina ◽  
Brunello Tirozzi ◽  
Camillo Tassi
Keyword(s):  
Free Energy ◽  
Long Range ◽  
Thermodynamic Limit ◽  
Random Variables ◽  
Hopfield Model ◽  
Xy Model ◽  
One Dimensional ◽  
Random Interaction ◽  
Independent Identically Distributed

We find the free-energy in the thermodynamic limit of a one-dimensional XY model associated to a system of N qubits. The coupling among the σ i z is a long range two-body random interaction. The randomness in the couplings is the typical interaction of the Hopfield model with p patterns ( p < N ), where the patterns are p sequences of N independent identically distributed random variables (i.i.d.r.v.), assuming values ± 1 with probability 1 / 2 . We show also that in the case p ≤ α N , α ≠ 0 , the free-energy is asymptotically independent from the choice of the patterns, i.e., it is self-averaging.

scholarly journals Remarks on the Interpolation Method

2020 ◽  
Vol 181 (4) ◽  
pp. 1218-1238
Author(s):  
Roberto Boccagna ◽  
Davide Gabrielli
Keyword(s):  
Free Energy ◽  
Thermodynamic Limit ◽  
Spin Glasses ◽  
Interpolation Method ◽  
Mean Field ◽  
Random Variables ◽  
Gaussian Random Variables ◽  
Mean Field Spin Glasses

Abstract We discuss a generalization of the classic condition of validity of the interpolation method for the density of quenched free energy of mean field spin glasses. The condition is written just in terms of the $$L^2$$ L 2 metric structure of the Gaussian random variables. As an example of application we deduce the existence of the thermodynamic limit for a GREM model with infinite branches for which the classic conditions of validity fail. We underline the dependence of the density of quenched free energy just on the metric structure and discuss the models from a metric viewpoint.

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