Generalized Gross-Neveu Universality Class with Non-Abelian Symmetry

We use the large N critical point formalism to compute d-dimensional critical exponents at several orders in 1/N in an Ising Gross-Neveu universality class where the core interaction includes a Lie group generator. Specifying a particular symmetry group or taking the abelian limit of the final exponents recovers known results but also provides expressions for any Lie group or fermion representation.

New Solutions of the Heat Equation and Application to Thin Plate Heat Conduction

Using a Lie symmetry group generator and a generalised form of Euler’s formula for solving second order ordinary differential equations, we determine new symmetries for the heat equation, leading to new solutions. As an application, we test a formula resulting from this approach on thin plate heat conduction