scholarly journals Microcanonical Entropy of the Infinite-State Potts Model

2011 ◽  
Vol 2011 ◽  
pp. 1-5 ◽  
Author(s):  
Jonas Johansson ◽  
Mats-Erik Pistol
Keyword(s):  
Density Of States ◽  
Thermodynamic Limit ◽  
Potts Model ◽  
Direct Consequence ◽  
Configurational Energy ◽  
First Order ◽  
Entire Energy Range ◽  
Straight Line ◽  
First Order Transition ◽  
Infinite State

In this investigation we show that the entropy of the two-dimensional infinite-state Potts model is linear in configurational energy in the thermodynamic limit. This is a direct consequence of the local convexity of the microcanonical entropy, associated with a finite system undergoing a first-order transition. For a sufficiently large number of states , this convexity spans the entire energy range of the model. In the thermodynamic limit, the convexity becomes insignificant, and the microcanonical entropy (the logarithm of the density of states) tends to a straight line. In order to demonstrate the behaviour of the convexity, we use the Wang-Landau Monte-Carlo technique to numerically calculate the density of states for a few finite but high values of . Finally, we calculate the free energy and discuss the generality of our results.

scholarly journals Ferroic Multipolar Order and Disorder in Cyanoelpasolite Molecular Perovskites

2018 ◽  
Author(s):  
Chloe Coates ◽  
Harry Gray ◽  
Johnathan Bulled ◽  
Hanna Boström ◽  
Arkadiy Simonov ◽  
...  
Keyword(s):  
Potts Model ◽  
Degrees Of Freedom ◽  
Variable Temperature ◽  
First Order ◽  
Order And Disorder ◽  
Simple Cubic ◽  
Different Types ◽  
Mechanical Models ◽  
Statistical Mechanical ◽  
First Order Transition

<div>We use a combination of variable-temperature high-resolution synchrotron X-ray powder diffraction measurements and Monte Carlo simulations to characterise the evolution of two different types of ferroic multipolar order in a series of cyano elpasolite molecular perovskites. We show that ferroquadrupolar order in [C3N2H5]2Rb[Co(CN)6] is a first-order process that is well described by a 4-state Potts model on the simple cubic lattice. Likewise, ferrooctupolar order in [NMe4]2B[Co(CN)6] (B = K, Rb, Cs) also emerges via a first-order transition that now corresponds to a 6-state Potts model. Hence, for these particular cases, the dominant symmetry breaking mechanisms are well understood in terms of simple statistical mechanical models. By varying composition, we find that the effective coupling between multipolar degrees of freedom—and hence the temperature at which ferromultipolar order emerges—can be tuned in a chemically sensible manner.</div><div><br></div>

Finite Size Scaling of Metastability in First Order Transitions

1998 ◽  
Vol 12 (20) ◽  
pp. 2063-2066 ◽  
Author(s):  
Smita Ota ◽  
S. B. Ota
Keyword(s):  
Monte Carlo ◽  
Potts Model ◽  
Linear Dimension ◽  
Finite Size ◽  
System Size ◽  
Xy Model ◽  
Finite Size Scaling ◽  
First Order ◽  
First Order Transition ◽  
Physical Quantities

Microcanonical Monte Carlo simulations have been carried out for the extended 2d XY-model and the 2d q=10 state Potts model undergoing first order transitions. It has been found that the temperature dependence of the physical quantities exhibit "S"-shaped nature at the first order transition. The excursion into the metastable branch is found to increase by reducing the system size. The metastability is found to scale with the linear dimension of the system.

scholarly journals Ferroic multipolar order and disorder in cyanoelpasolite molecular perovskites

2019 ◽  
Vol 377 (2149) ◽  
pp. 20180219 ◽  
Author(s):  
C. S. Coates ◽  
H. J. Gray ◽  
J. M. Bulled ◽  
H. L. B. Boström ◽  
A. Simonov ◽  
...  
Keyword(s):  
Potts Model ◽  
Degrees Of Freedom ◽  
Variable Temperature ◽  
First Order ◽  
Order And Disorder ◽  
Simple Cubic ◽  
Different Types ◽  
Mechanical Models ◽  
Statistical Mechanical ◽  
First Order Transition

We use a combination of variable-temperature high-resolution synchrotron X-ray powder diffraction measurements and Monte Carlo simulations to characterize the evolution of two different types of ferroic multipolar order in a series of cyanoelpasolite molecular perovskites. We show that ferroquadrupolar order in [C 3 N 2 H 5 ] 2 Rb[Co(CN) 6 ] is a first-order process that is well described by a four-state Potts model on the simple cubic lattice. Likewise, ferrooctupolar order in [NMe 4 ] 2 B[Co(CN) 6 ] (B = K, Rb, Cs) also emerges via a first-order transition that now corresponds to a six-state Potts model. Hence, for these particular cases, the dominant symmetry breaking mechanisms are well understood in terms of simple statistical mechanical models. By varying composition, we find that the effective coupling between multipolar degrees of freedom—and hence the temperature at which ferromultipolar order emerges—can be tuned in a chemically sensible manner. This article is part of the theme issue ‘Mineralomimesis: natural and synthetic frameworks in science and technology’.

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