Microcanonical Monte Carlo simulations of the first-order transition in the two-dimensional Potts model

Abstract

Microcanonical Monte Carlo simulations have been implemented in the two-dimensional (2D) q -state Potts model. The ergodicity of this simulation technique for the Potts model is studied. It does not seem to depend on the value of q . A lack of ergodicity for small values of the system energy is reported and discussed. It has been found that the temperature dependences of physical quantities exhibit an `S'-shaped nature at the first-order transition. The degree of `S'-shaped nature was enhanced by increasing q and reducing the system size. We believe on the basis of our computer simulations that the `S' shape represents the equilibrium behaviour of a finite isolated system.

Continuous phase transitions with a convex dip in the microcanonical entropy

“…The behaviour of the specific heat is completely different if the system undergoes a discontinuous phase transition. In this case the microcanonical entropy density of a finite system has a convex dip which leads to a negative microcanonical specific heat for a certain energy interval [5,28,29,30,31,32,33]. This is different in the canonical ensemble where the specific heat, which is related to the variance of the energy, is always positive for any finite system.…”

“…The associated singularities, however, are not the consequence of a non-analytic microcanonical entropy and can therefore be characterized by classical critical exponents [19,22]. Similarly, intriguing features are also revealed in the microcanonical entropy of small systems with a discontinuous transition in the infinite volume limit [5,28,29,30,31,32,33]. A typical back-bending of the microcanonical caloric curve is observed, leading to a negative heat capacity.…”

Microcanonical Monte Carlo Simulation of 2D 4-State Potts Model

“…This demon energy when added to the system energy . Since the system energy is discrete we find the following equation valid for Potts model to determine the system temperature from the average demon energy [11].…”

Qualitative Picture of Scaling in the Entropy Formalism

“…The thermal properties of a system can also be investigated in a reduced entropy formalism. Indeed, this formalism has been used extensively in the past to study the behaviour of systems by means of the microcanonical entropy [7][8][9][10]12]. The reduced entropy of the infinite system is defined by…”

“…The description of phase transitions in the entropy or microcanonical formalism has gained growing interest in recent years [5][6][7][8][9][10][11][12][13][14][15][16]18]. Apart from the study of discontinuous transitions in spin systems some works also investigated continuous phase transitions in the microcanonical approach [11,14,16,17,19,20].…”