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An emended and improved version of the present paper has been archived in math-ph/0505057, and a preliminary account of its content has been published in Phys.Rev.Lett. 92, 60601, (2004). Moreover, in order to prove the relevance of topology for phase transition phenomena in a broad domain of physically interesting cases, we have proved another theorem which is reported in math-ph/0505058 and which is crucially based on the result of the paper archived in math-ph/0505057.
Inverse phase transitions are striking phenomena in which an apparently more ordered state disorders under cooling. This behavior can naturally emerge in tricritical systems on heterogeneous networks and it is strongly enhanced by the presence of dis
A new nonlinear integral equation (NLIE) describing the thermodynamics of the Heisenberg spin chain is derived based on the t-W relation of the quantum transfer matrices. The free energy of the system in a magnetic field is thus obtained by solving t
Inspired by Fr{o}hlich-Spencer and subsequent authors who introduced the notion of contour for long-range systems, we provide a definition of contour and a direct proof for the phase transition for ferromagnetic long-range Ising models on $mathbb{Z}^
A unified description of i) classical phase transitions and their remnants in finite systems and ii) quantum phase transitions is presented. The ensuing discussion relies on the interplay between, on the one hand, the thermodynamic concepts of temper
The dimer model on a strip is considered as a Yang-Baxter mbox{integrable} six vertex model at the free-fermion point with crossing parameter $lambda=tfrac{pi}{2}$ and quantum group invariant boundary conditions. A one-to-many mapping of vertex onto