The Hierarchical Random Energy Model
نویسندگان
چکیده
We introduce a Random Energy Model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a nonmean field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin glass condensation transition similar to the one occurring in the usual mean field Random Energy Model. At variance with mean field, the high temperature branch of the free-energy is non-analytic at the transition point.
منابع مشابه
Energy Optimization of Under-actuated Crane model for Time-Variant Load Transferring using Optimized Adaptive Combined Hierarchical Sliding Mode Controller
This paper designs an Optimized Adaptive Combined Hierarchical Sliding Mode Controller (OACHSMC) for a time-varying crane model in presence of uncertainties. Uncertainties have always been one of the most important challenges in designing control systems, which include the unknown parameters or un-modeled dynamics in the systems. Sliding mode controller (SMC) is able to compensate the system in...
متن کاملHierarchical random energy model of a spin glass.
We introduce a random energy model on a hierarchical lattice where the interaction strength between variables is a decreasing function of their mutual hierarchical distance, making it a non-mean-field model. Through small coupling series expansion and a direct numerical solution of the model, we provide evidence for a spin-glass condensation transition similar to the one occurring in the usual ...
متن کاملIRWIN AND JOAN JACOBS CENTER FOR COMMUNICATION AND INFORMATION TECHNOLOGIES The Generalized Random Energy Model of Spin Glasses and its Application to the Statistical Physics of Code Ensembles with Hierarchical Structures
In an earlier work, the statistical physics associated with finite–temperature decoding of code ensembles, along with the relation to their random coding error exponents, were explored in a framework that is analogous to Derrida’s random energy model (REM) of spin glasses, according to which the energy levels of the various spin configurations are independent random variables. The generalized R...
متن کاملTesting Multidimensional and Hierarchical Model of School Motivation Questionnaire
Abstract Objective: One of the theories that motivation into a multi-objective model considers, Mayer's theory of personal investment. This theory is a useful framework for evaluating multi-dimensional and hierarchical nature of goal provides the motivation. The aim of this study is to investigate a multi-dimensional and hierarchical structure of achievement goal orientation. Methods: The popul...
متن کاملStatistical mechanical analysis of a hierarchical random code ensemble in signal processing
Abstract. We study a random code ensemble with a hierarchical structure, which is closely related to the generalized random energy model with discrete energy values. Based on this correspondence, we analyze the hierarchical random code ensemble by using the replica method in two situations: lossy data compression and channel coding. For both the situations, the exponents of large deviation anal...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
عنوان ژورنال:
دوره شماره
صفحات -
تاریخ انتشار 2009