scholarly journals Phase transition in a stochastic geometry model with applications to statistical mechanics

2021 ◽  
Author(s):  
O. Kazemi ◽  
A. Pourdarvish ◽  
J. Sadeghi
Keyword(s):  
Phase Transition ◽  
Statistical Mechanics ◽  
Stochastic Geometry ◽  
Probability Function ◽  
Dimensional Space ◽  
Connected Components ◽  
Thermodynamic Quantities ◽  
Geometry Model ◽  
Physics Literature ◽  
Approximate Probability

We study the connected components of the stochastic geometry model on Poisson points which is obtained by connecting points with a probability that depends on their relative position. Equivalently, we investigate the random clusters of the ran- dom connection model defined on the points of a Poisson process in d-dimensional space where the links are added with a particular probability function. We use the thermodynamicrelationsbetweenfreeenergy,entropyandinternalenergytofindthe functions of the cluster size distribution in the statistical mechanics of extensive and non-extensive. By comparing these obtained functions with the probability function predicted by Penrose, we provide a suitable approximate probability function. More- over, we relate this stochastic geometry model to the physics literature by showing how the fluctuations of the thermodynamic quantities of this model correspond to other models when a phase transition (10.1002/mma.6965, 2020) occurs. Also, we obtain the critical point using a new analytical method.

scholarly journals Gluodynamics and deconfinement phase transition under rotation from holography

2021 ◽  
Vol 2021 (7) ◽  
Author(s):  
Xun Chen ◽  
Lin Zhang ◽  
Danning Li ◽  
Defu Hou ◽  
Mei Huang
Keyword(s):  
Phase Transition ◽  
Angular Velocity ◽  
Chemical Potential ◽  
Entropy Density ◽  
Thermodynamic Quantities ◽  
Strongly Coupled ◽  
Trace Anomaly ◽  
Holographic Qcd ◽  
Deconfinement Phase Transition ◽  
Small Chemical

Abstract We investigate rotating effect on deconfinement phase transition in an Einstein-Maxwell-Dilaton (EMD) model in bottom-up holographic QCD approach. By constructing a rotating black hole, which is supposed to be dual to rotating strongly coupled nuclear matter, we investigate the thermodynamic quantities, including entropy density, pressure, energy density, trace anomaly, sound speed and specific heat for both pure gluon system and two-flavor system under rotation. It is shown that those thermodynamic quantities would be enhanced by large angular velocity. Also, we extract the information of phase transition from those thermodynamic quantities, as well as the order parameter of deconfinement phase transition, i.e. the loop operators. It is shown that, in the T − ω plane, for two-flavor case with small chemical potential, the phase transition is always crossover. The transition temperature decreases slowly with angular velocity and chemical potential. For pure gluon system with zero chemical potential, the phase transition is always first order, while at finite chemical potential a critical end point (CEP) will present in the T − ω plane.

The Order of Phase Transition of Solvable DNA Melting Models

2003 ◽  
Vol 17 (16) ◽  
pp. 885-896 ◽  
Author(s):  
Su-Long Nyeo ◽  
I-Ching Yang
Keyword(s):  
Phase Transition ◽  
Hydrogen Bonds ◽  
Short Range ◽  
Scaling Laws ◽  
Dna Melting ◽  
Thermodynamic Quantities ◽  
Base Pairs ◽  
Order Of Phase Transition ◽  
Exactly Solvable ◽  
Dna Models

The phase transition of DNA molecules is studied in an exactly solvable formalism with the Morse and Deng–Fan potentials for the interstrand hydrogen bonds of nucleotide base pairs. It is shown that although the two potentials have different short-range behaviors, the thermodynamic quantities of the DNA system in these potentials enjoy the same scaling laws with the associated critical exponents, which are explicitly calculated. These exactly solvable DNA models are shown to exhibit a phase transition of the second order and the results of the analysis agree with previous studies.

scholarly journals Phase diagram of the selfinteracting particle­-antiparticle boson system

2021 ◽  
Vol 29 (1) ◽  
pp. 5-14
Author(s):  
D. Anchishkin ◽  
V. Gnatovskyy ◽  
D. Zhuravel ◽  
V. Karpenko
Keyword(s):  
Phase Transition ◽  
Phase Diagram ◽  
Phase Diagrams ◽  
Canonical Ensemble ◽  
Bose Condensate ◽  
Mean Field ◽  
Thermodynamic Quantities ◽  
Boson System ◽  
The Mean

A system of interacting relativistic bosons at finite temperatures and isospin densities is studied within the framework of the Skyrme­like mean­field model. The mean field contains both attractive and repulsive terms. The consideration is taken within the framework of the Canonical Ensemble and the isospin­density dependencies of thermodynamic quantities is obtained, in particular as the phase diagrams. It is shown that in such a system, in addition to the formation of a Bose­Einstein condensate, a liquid­gas phase transition is possible. We prove that the multi­boson system develops the Bose condensate for particles of high­density component only.

scholarly journals Phase Transition in Modified Newtonian Dynamics (MONDian) Self-Gravitating Systems

Entropy ◽  
2021 ◽  
Vol 23 (9) ◽  
pp. 1158
Author(s):  
Mohammad Hossein Zhoolideh Zhoolideh Haghighi ◽  
Sohrab Rahvar ◽  
Mohammad Reza Rahimi Rahimi Tabar
Keyword(s):  
Phase Transition ◽  
Binary Systems ◽  
Dimensional Space ◽  
Gravitational Interaction ◽  
Three Dimensional ◽  
Physical Parameters ◽  
Canonical Systems ◽  
Modified Newtonian Dynamics ◽  
Newtonian Dynamics ◽  
Gravitating Systems

We study the statistical mechanics of binary systems under the gravitational interaction of the Modified Newtonian Dynamics (MOND) in three-dimensional space. Considering the binary systems in the microcanonical and canonical ensembles, we show that in the microcanonical systems, unlike the Newtonian gravity, there is a sharp phase transition, with a high-temperature homogeneous phase and a low-temperature clumped binary one. Defining an order parameter in the canonical systems, we find a smoother phase transition and identify the corresponding critical temperature in terms of the physical parameters of the binary system.

Order, Symmetry, and the Organization of Matter

2013 ◽  
Author(s):  
Daniel L. Stein ◽  
Charles M. Newman
Keyword(s):  
Phase Transition ◽  
Statistical Mechanics ◽  
Ground State ◽  
Order Parameter ◽  
Condensed Matter ◽  
Broken Symmetry ◽  
Essential Ingredient ◽  
Important Concept ◽  
Basic Concepts ◽  
Thermodynamics And Statistical Mechanics

This chapter introduces the basic concepts and language that will be needed later on: order, symmetry, invariance, broken symmetry, Hamiltonian, condensed matter, order parameter, ground state, and several thermodynamic terms. It also presents the necessary concepts from thermodynamics and statistical mechanics that will be needed later. It boils down the latter to its most elemental and essential ingredient: that of temperature as controlling the relative probabilities of configurations of different energies. For much of statistical mechanics, all else is commentary. This is sufficient to present an intuitive understanding of why and how matter organizes itself into different phases as temperature varies, and leads to the all-important concept of a phase transition.

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