A constant thermodynamic tension Monte Carlo method is introduced and applied studies of the elastic properties of a two-dimensional system of hard cyclic hexamers. Elastic compliances and elastic constants are determined at a number of different values of the pressure. The existence of the phase transition between a tilted and a straight phase is confirmed. The results obtained strongly suggest that the Poisson modulus can be negative in the tilted phase.

The role of negative compressibility is considered in detail. Experimental observations of negative bulk modulus in pre‐strained foam are presented and interpreted. A constrained microscopic model which exhibits negative compressibility is proposed. Some other negative and counterintuitive properties of matter, like negative Poisson's ratio, negative thermal expansion, negative specific heat, and negative pressure are also discussed. A simple thermodynamic model with negative thermal expansion is presented.

A two-dimensional system of hard cyclic hexamers is shown to display an anomalous (negative) Poisson ratio in a high-density crystalline phase. The anomaly can be reproduced qualitatively by a simple free-volume (FV) approximation. The FV approximation and a lattice model indicate the crucial role of broken mirror symmetry for this phenomenon.