Regensburg 2025 – scientific programme

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DY: Fachverband Dynamik und Statistische Physik

DY 22: Poster: Statistical Physics

DY 22.9: Poster

Wednesday, March 19, 2025, 10:00–12:00, P3

Residual entropy of ice: A study based on transfer matrices — •De-Zhang Li¹, Yu-Jie Cen², Xin Wang³, and Xiao-Bao Yang⁴ — ¹Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area — ²Institute of Materials Chemistry, Vienna University of Technology — ³Department of Physics, City University of Hong Kong — ⁴Department of Physics, South China University of Technology

The residual entropy of ice systems has long been a significant and intriguing issue in condensed-matter physics and statistical mechanics. This study focuses on two typical realistic ice systems: hexagonal ice (ice Ih) and cubic ice (ice Ic). We present a transfer-matrix description of the number of ice-ruled configurations for these systems. A transfer matrix M is constructed for ice Ic, where each element represents the number of ice-ruled configurations of a hexagonal monolayer under certain conditions. The product of M and M^T corresponds to a bilayer unit in the ice Ih lattice, thus forming an exact transfer matrix for ice Ih. Utilizing this, we show that the residual entropy of ice Ih is not less than that of ice Ic in the thermodynamic limit, first proved by Onsager in the 1960s. Additionally, we introduce an alternative transfer matrix M′ for ice Ih based on a monolayer periodic unit. Various interesting properties of M, MM^T and M′ are analyzed, including the sum of all elements, the element in the first row and first column, and the trace. Each property corresponds to the residual entropy of a certain 2-d ice model. This work provides an effective description, based on transfer matrices, for the residual entropies of various 2-d ice models.

Keywords: residual entropy; real ice; transfer matrix; two-dimensional ice model; six-vertex model