On a conjecture of C.N. Yang

Yonathan Shapir

A Hamiltonian approach to the monomer-dimer model is derived by a special truncation of the spin operators in the Yang-Lee model. At its critical point, the negative fugacity dimer problem is proved to belong to the universality class of the Yang-Lee singularity as previously conjectured.

William Demopoulos

Guillaume Lang

In this paper, we apply experimental number theory to two integrable quantum models in one dimension, the Lieb-Liniger Bose gas and the Yang-Gaudin Fermi gas with contact interactions. We identify patterns in weak- and strong-coupling series expansions of the ground-state energy, local correlation functions and pressure. Based on the most accurate data available in the literature, we make a few conjectures about their mathematical structure and extrapolate to higher orders

Gianni Cassinelli, Ernesto De Vito, PEKKA J. LAHTI +1 more

Andrew Lenard

R. J. Baxter, S. K. Tsang

Metcalf and Yang (1978) have obtained the numerical estimate 0.3333 k for the entropy per site of hard hexagons. They therefore conjecture that the exact value is k/3. The authors have used the corner transfer matrix method to obtain a more accurate numerical estimate, namely 0.333 242 721 976 k, which contradicts the conjecture. The problem is a good example of the numerical accuracy of the method.