On the mean-field spherical model
نویسندگان
چکیده
Exact solutions are obtained for the mean-field spherical model, with or without an external magnetic field, for any finite or infinite number N of degrees of freedom, both in the microcanonical and in the canonical ensemble. The canonical result allows for an exact discussion of the loci of the Fisher zeros of the canonical partition function. The microcanonical entropy is found to be nonanalytic for arbitrary finite N . The mean-field spherical model of finite size N is shown to be equivalent to a mixed isovector/isotensor σ-model on a lattice of two sites. Partial equivalence of statistical ensembles is observed for the mean-field spherical model in the thermodynamic limit. A discussion of the topology of certain state space submanifolds yields insights into the relation of these topological quantities to the thermodynamic behavior of the system in the presence of ensemble nonequivalence.
منابع مشابه
Modeling of Fault Co-seismic Displacement Fields in Elastic Environments Based on Spherical Dislocation Theory
This research is based on the modeling of co-seismic deformations due to the fault movement in the elastic environments, and we can obtain the deformations generated in the faults. Here, modeling of the co-seismic displacement field is based on the analytical method with two spherical dislocation model and half-space dislocation model. The difference in displacement field from two spherical and...
متن کاملApplying Spatial Geostatistical Analysis Models for Evaluating Variability of Soil Properties in Eastern Shiraz, Iran
ABSTRACT- The information on the spatial properties of soil is vital to improve soil management and to increase the crop productivity. Geostatistical analysis technique is one of the most important methods for determining the spatial properties of soil. The aim of this study was to investigate spatial variability of soil chemical and physical attributes for field management in eastern Shiraz, I...
متن کاملModeling thermodynamic properties of electrolytes: Inclusion of the mean spherical approximation (MSA) in the simplified SAFT equation of state
In this work, an equation of state has been utilized for thermodynamic modeling of aqueous electrolyte solutions. The proposed equation of state is a combination of simplified statistical associating fluid theory (SAFT) equation of state (similar to simplified PC-SAFT) to describe the effect of short-range interactions and mean spherical approximation (MSA) term to describe the effect of long-r...
متن کاملRegression Modeling for Spherical Data via Non-parametric and Least Square Methods
Introduction Statistical analysis of the data on the Earth's surface was a favorite subject among many researchers. Such data can be related to animal's migration from a region to another position. Then, statistical modeling of their paths helps biological researchers to predict their movements and estimate the areas that are most likely to constitute the presence of the animals. From a geome...
متن کاملEstimation of the Stress Intensity Factors for Surface Cracks in Spherical Electrode Particles Subject to Phase Separation
Experiments have frequently shown that phase separation in lithium-ion battery electrodes could lead to the formation of mechanical defects, hence causing capacity fading. The purpose of the present work has been to examine stress intensity factors for pre-existing surface cracks in spherical electrode particles during electrochemical deintercalation cycling using both analytical and numerical ...
متن کامل