Uncovering the secrets of unusual phase diagrams: applications of two-dimensional Wang-Landau sampling

Abstract

We use a two-dimensional Wang-Landau sampling algorithm to calculate the density of states for two discrete spin models and then extract their phase diagrams. The first system is an asymmetric Ising model on a triangular lattice with two-and three-body interactions in an external field. An accurate density of states allows us to locate the critical endpoint accurately in a two-dimensional parameter space. We observe a divergence of the spectator phase boundary and of the temperature derivative of the magnetization coexistence diameter at the critical endpoint in quantitative agreement with theoretical predictions. The second model is a Q-state Potts model in an external field H. We map the phase diagram of this model for Q ≥ 8 and observe a first-order phase transition line that starts at the H = 0 phase transition point and ends at a critical point (T c , H c ), which must be located in a two-dimensional parameter space. The critical field H c (Q) is positive and increases with Q, in qualitative agreement with previous theoretical predictions.

QUALITATIVE ASPECTS OF THE PHASE DIAGRAM OF J1–J2 MODEL ON THE CUBIC LATTICE

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Thermodynamics of a conformational change using a random walk in energy-reaction coordinate space: Application to methane dimer hydrophobic interactions

“…The algorithm of a random walk to extract the JDOS is better known for calculations of thermal averages. [19][20][21][22][23][24][25][26] Apparently the JDOS algorithm for ͑r , E͒ variables is a promising tool for calculations of the thermodynamics of conformational changes as well. 25 The JDOS algorithm is a straightforward extension of the original Wang-Landau ͑WL͒ sampling algorithm.…”

New Wang-Landau approach to obtain phase diagrams for multicomponent alloys

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