# Dipolar Dimer Liquid

## TL;DR

This paper introduces a model of dipolar dimer liquid on a 2D lattice, revealing a partially ordered glacia phase at high density and low temperature, with insights into entropy and phase transitions relevant to hydrophobic effects.

## Contribution

It proposes a novel dipolar dimer liquid model, maps phase transitions to an annealed Ising model, and explores entropy effects related to polymers and biological phenomena.

## Key findings

- Identification of a glacia phase at high density and low temperature.
- Critical temperature estimation aligning with Ising model bounds.
- Power-law suppression of configurational entropy with polymer length.

## Abstract

A model of dipolar dimer liquid (DDL) on a two-dimensional lattice has been proposed. We found that at high density and low temperature, it has a partially ordered phase which we called glacia phase. The glacia phase transition can be understood by mapping the DDL to an annealed Ising model on random graphs. In the high density limit the critical temperature obtained by the Monte Carlo simulation is $k_BT_c^G = (3.5\pm0.1)J$, which agrees with the estimations of the upper and lower bounds of $k_BT_c^G$ with exactly solved Ising models. In the high density and low temperature limit, we further studied configurational entropy of the DDL in the presence of the neutral polymers. The suppression of the configurational entropy scales as a power law of the polymer length $\lambda_p^\alpha$ with $\alpha \geq 1$, which implies that the configurational entropy of water plays essential roles in understanding the hydrophobic effect and the protein folding problem.