Inflection points of microcanonical entropy: Monte Carlo simulation of q state Potts model on a finite square lattice
Abstract
Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an Sshape with a minimum and maximum around the point of inflexion for the case of first order transition.
 Authors:

 Department of Physics, Pondicherry University, Puducherry605014 (India)
 Publication Date:
 OSTI Identifier:
 22269261
 Resource Type:
 Journal Article
 Journal Name:
 AIP Conference Proceedings
 Additional Journal Information:
 Journal Volume: 1591; Journal Issue: 1; Conference: 58. DAE solid state physics symposium 2013, Patiala, Punjab (India), 1721 Dec 2013; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA); Journal ID: ISSN 0094243X
 Country of Publication:
 United States
 Language:
 English
 Subject:
 75 CONDENSED MATTER PHYSICS, SUPERCONDUCTIVITY AND SUPERFLUIDITY; 37 INORGANIC, ORGANIC, PHYSICAL AND ANALYTICAL CHEMISTRY; COMPUTERIZED SIMULATION; ENERGY DENSITY; ENTROPY; MONTE CARLO METHOD; PHASE TRANSFORMATIONS; PROTEINS; TETRAGONAL LATTICES; TRANSITION TEMPERATURE
Citation Formats
Praveen, E., Email: svmstaya@gmail.com, and Satyanarayana, S. V. M.,. Inflection points of microcanonical entropy: Monte Carlo simulation of q state Potts model on a finite square lattice. United States: N. p., 2014.
Web. doi:10.1063/1.4872512.
Praveen, E., Email: svmstaya@gmail.com, & Satyanarayana, S. V. M.,. Inflection points of microcanonical entropy: Monte Carlo simulation of q state Potts model on a finite square lattice. United States. https://doi.org/10.1063/1.4872512
Praveen, E., Email: svmstaya@gmail.com, and Satyanarayana, S. V. M.,. Thu .
"Inflection points of microcanonical entropy: Monte Carlo simulation of q state Potts model on a finite square lattice". United States. https://doi.org/10.1063/1.4872512.
@article{osti_22269261,
title = {Inflection points of microcanonical entropy: Monte Carlo simulation of q state Potts model on a finite square lattice},
author = {Praveen, E., Email: svmstaya@gmail.com and Satyanarayana, S. V. M.,},
abstractNote = {Traditional definition of phase transition involves an infinitely large system in thermodynamic limit. Finite systems such as biological proteins exhibit cooperative behavior similar to phase transitions. We employ recently discovered analysis of inflection points of microcanonical entropy to estimate the transition temperature of the phase transition in q state Potts model on a finite two dimensional square lattice for q=3 (second order) and q=8 (first order). The difference of energy density of states (DOS) Δ ln g(E) = ln g(E+ ΔE) −ln g(E) exhibits a point of inflexion at a value corresponding to inverse transition temperature. This feature is common to systems exhibiting both first as well as second order transitions. While the difference of DOS registers a monotonic variation around the point of inflexion for systems exhibiting second order transition, it has an Sshape with a minimum and maximum around the point of inflexion for the case of first order transition.},
doi = {10.1063/1.4872512},
url = {https://www.osti.gov/biblio/22269261},
journal = {AIP Conference Proceedings},
issn = {0094243X},
number = 1,
volume = 1591,
place = {United States},
year = {2014},
month = {4}
}