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Random matrix theory and critical phenomena in spin models
Supervisor: Francesco Mezzadri
Theme: Random Matrix
Recent studies have shown that random matrix theory can give new insight into the understanding of phase transitions in lattice systems. The problems to address include the behaviour of entanglement in the ground state of quantum spin chains, the study of universality of critical exponents and of the scaling hypothesis in two dimensional spin models. Thermodynamics variables in proximity of critical temperatures obey power laws whose exponents seem to depend only on the dimensionality and symmetries of the system; the scaling hypothesis, instead, asserts that the thermodynamic properties of a macroscopic system depend only on few relevant variables that characterize its behaviour on a particular time or
length scale.