Statistical Symmetries in Random Fields

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Conformal Transformations: Theory and Applications

Explores the theory and applications of conformal transformations, covering special conformal transformations and isomorphic transformations.

Quantum Statistics: Canonical & Grand Canonical Ensembles

Explores quantum statistics in canonical and grand canonical ensembles, discussing distinguishability, microstates, and the Pauli exclusion principle.

2D Transformations: Linear Maps & Matrices

Covers 2D transformations, linear maps, matrices, affine transformations, and orthogonal transformations.

Monte Carlo Simulations

Covers Monte Carlo simulations, ensemble properties, and numerical integration techniques.

Paramagnetism: Microcanonical vs Canonical Treatment

Delves into the microcanonical and canonical treatment of paramagnetism in external fields.

Perfect Gas: Microcanonical Ensemble

Covers the microcanonical ensemble, phase space, and the equation of a perfect gas.

Universality and Rotational Invariance in Isoradial Graphs

Covers universality and rotational invariance in isoradial graphs and their implications in statistical mechanics.

Renormalization & Scaling

Explores renormalization, scaling, critical points, exponents, and phase transitions in conformal field theory and quantum gravity.

Ring Polymer Molecular Dynamics

Covers Ring Polymer Molecular Dynamics, quantum statistics, chemical reaction rates, and condensed phase problems.

Grand Canonical and Isothermal Ensembles

Explores the grand canonical and isothermal isobaric ensembles and their thermodynamic implications.