Statistical mechanics, gravity, and Euclidean theory

Statistical Mechanics and Information Theory

Definition 1 (Spin Excess) For a system with N particles with spins ±m, the spin excess is given by how many particles more than N/2 have spin +m, i.e. S = N↑ − N2 where N↑ is the number of particles with spin +m. From Definition 1 and Equation (1) it follows that the total magnetic moment is given by M = 2mS. Theoretically, one could calculate the system’s magnetic moment at some point in time...

The P ( d ) , Euclidean quantum field theory as classical statistical mechanics

To date in constructive field theory, two types of ultraviolet cutoffs have been used [32]: 1) A smeared field, i.e., g(x) is replaced by $,(x) = \ h(x y)$(y)dy, where h is some smooth positive approximation to the delta function; 2) Box and sharp momentum cutoff, i.e., g(x) is replaced by the periodic field Q ~ , ~ ( X ) , which is obtained by approximating the Fourier integral defining g(x) b...

The Statistical Mechanics of the Three-Dimensional Euclidean Black Hole

In its formulation as a Chern-Simons theory, threedimensional general relativity induces a Wess-Zumino-Witten action on spatial boundaries. Treating the horizon of the three-dimensional Euclidean black hole as a boundary, I count the states of the resulting WZW model, and show that they yield the correct Bekenstein-Hawking entropy. The relevant states can be understood as “would-be gauge” degre...

A Statistical Mechanics Approach to Random Euclidean MAX TSP

Conformal Field Theory and Statistical Mechanics∗