Mean field statistical mechanics of model Hamiltonian for hydrogen bonded phase transitions

2008 ◽  
Vol 246 (2) ◽  
pp. 376-382 ◽  
Author(s):  
Mohd Mustaqim Rosli ◽  
Beck Sim Lee ◽  
Hoong Kun Fun
Keyword(s):  
Phase Transitions ◽  
Statistical Mechanics ◽  
Mean Field ◽  
Model Hamiltonian ◽  
Bonded Phase ◽  
Hydrogen Bonded

scholarly journals Nuclear Shell Model And Quantum Phase Transitions

2019 ◽  
Vol 26 ◽  
pp. 88
Author(s):  
S. Karampagia ◽  
V. Zelevinsky
Keyword(s):  
Phase Transition ◽  
Phase Transitions ◽  
Shell Model ◽  
Quantum Phase Transitions ◽  
Mean Field ◽  
Nuclear Shell Model ◽  
Matrix Elements ◽  
Model Hamiltonian ◽  
Orbital Space ◽  
Nuclear Shell

The usual nuclear shell model defines nuclear properties through an effective mean-field plus a two-body interaction Hamiltonian in a finite orbital space. In this study we try to understand the correlation between the various parts of the shell model Hamiltonian and the nuclear observables and collectivity in nuclei. By varying specific groups of matrix elements we find signs of a phase transition in nuclei between a non-collective and a collective phase. In all cases studied the collective phase is attained when the single-particle transfer matrix elements are dominant in the shell model Hamiltonian, giving collective characteristics to nuclei.

scholarly journals DYNAMIC DIPOLE AND QUADRUPOLE PHASE TRANSITIONS IN THE KINETIC SPIN-1 MODEL

2006 ◽  
Vol 17 (09) ◽  
pp. 1239-1255 ◽  
Author(s):  
MUSTAFA KESKİN ◽  
OSMAN CANKO ◽  
ERSIN KANTAR
Keyword(s):  
Magnetic Field ◽  
Phase Transitions ◽  
Phase Diagrams ◽  
Stochastic Dynamics ◽  
Mean Field ◽  
Dynamic Phase Transitions ◽  
Coexistence Phase ◽  
Dynamic Phase ◽  
Model Hamiltonian ◽  
Sinusoidal Magnetic Field

The dynamic phase transitions have been studied, within a mean-field approach, in the kinetic spin-1 Ising model Hamiltonian with arbitrary bilinear and biquadratic pair interactions in the presence of a time varying (sinusoidal) magnetic field by using the Glauber-type stochastic dynamics. The nature (first- or second-order) of the transition is characterized by investigating the behavior of the thermal variation of the dynamic order parameters. The dynamic phase transitions (DPTs) are obtained and the phase diagrams are constructed in the temperature and magnetic field amplitude plane and found six fundamental types of phase diagrams. Phase diagrams exhibit one or two dynamic tricritical points depending on the biquadratic interaction (K). Besides the disordered (D) and ferromagnetic (F) phases, the FQ + D, F + FQ and F + D coexistence phase regions also exist in the system and the F and F + D phases disappear for high values of K.

scholarly journals The structure of musical harmony as an ordered phase of sound: A statistical mechanics approach to music theory

2019 ◽  
Vol 5 (5) ◽  
pp. eaav8490 ◽  
Author(s):  
Jesse Berezovsky
Keyword(s):  
Phase Transitions ◽  
Statistical Mechanics ◽  
Music Theory ◽  
Mean Field ◽  
Field Approximation ◽  
Mean Field Approximation ◽  
Mean Field Model ◽  
Musical Harmony ◽  
Emergent Order ◽  
The Mean

Music, while allowing nearly unlimited creative expression, almost always conforms to a set of rigid rules at a fundamental level. The description and study of these rules, and the ordered structures that arise from them, is the basis of the field of music theory. Here, I present a theoretical formalism that aims to explain why basic ordered patterns emerge in music, using the same statistical mechanics framework that describes emergent order across phase transitions in physical systems. I first apply the mean field approximation to demonstrate that phase transitions occur in this model from disordered sound to discrete sets of pitches, including the 12-fold octave division used in Western music. Beyond the mean field model, I use numerical simulation to uncover emergent structures of musical harmony. These results provide a new lens through which to view the fundamental structures of music and to discover new musical ideas to explore.

Introduction

2017 ◽  
Author(s):  
Jochen Rau
Keyword(s):  
Probability Theory ◽  
Phase Transitions ◽  
Statistical Mechanics ◽  
Conservation Laws ◽  
Law Of Large Numbers ◽  
Macroscopic Scale ◽  
Classical Probability ◽  
Large Numbers ◽  
Microscopic World ◽  
New Phenomena

Statistical mechanics concerns the transition from the microscopic to the macroscopic realm. On a macroscopic scale new phenomena arise that have no counterpart in the microscopic world. For example, macroscopic systems have a temperature; they might undergo phase transitions; and their dynamics may involve dissipation. How can such phenomena be explained? This chapter discusses the characteristic differences between the microscopic and macroscopic realms and lays out the basic challenge of statistical mechanics. It suggests how, in principle, this challenge can be tackled with the help of conservation laws and statistics. The chapter reviews some basic notions of classical probability theory. In particular, it discusses the law of large numbers and illustrates how, despite the indeterminacy of individual events, statistics can make highly accurate predictions about totals and averages.

Phase transitions in physiologically-based multiscale mean-field brain models

2009 ◽  
pp. 179-201 ◽  
Author(s):  
P.A. Robinson ◽  
C.J. Rennie ◽  
A.J.K. Phillips ◽  
J.W. Kim ◽  
J.A. Roberts
Keyword(s):  
Phase Transitions ◽  
Mean Field ◽  
Physiologically Based ◽  
Brain Models
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