Séminaire des doctorants Tours
Partition function and six-vertex modelMatthieu Cornillault (Institut Denis Poisson Tours)
Thursday 19 February 2026 15:45 - Tours - E1180 (Salle de séminaire 1er étage E2)
Résumé :
The partition function is an important concept in statistical mechanics. For a system in contact with a thermostat, it allows us to compute its physical characteristics, such as the Helmholtz free energy, mean energy, entropy, and heat capacity.
Here, we are interested in the six-vertex model, which is a two-dimensional lattice with a coordination number of four. In this model, each vertex can have only six possible forms. Pauling introduced this model in 1935 to calculate the residual entropy of ice, and it can describe any crystal with hydrogen bonding.
In the late 1970s, the Quantum Inverse Scattering Method (QISM), also known as the algebraic Bethe ansatz, was invented. Within this framework, it was discovered that many quantum models, including the six-vertex model, which have completely different physical interpretations, can be described by different representations of the same algebra of operators. The partition function of the six-vertex model can be written with some elements of this algebra.
In this presentation, we will focus on a specific instance of this model: the rational six-vertex model with general boundary conditions. After presenting its general expression, we will discuss the thermodynamic limit of the model (when the lattice goes to infinity) and the resulting physical interpretations.
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