Partition function of free conformal higher spin theory

Irreversibility and Higher-spin Conformal Field Theory

I discuss the properties of the central charges c and a for higher-derivative and higher-spin theories (spin 2 included). Ordinary gravity does not admit a straightforward identification of c and a in the trace anomaly, because it is not conformal. On the other hand, higherderivative theories can be conformal, but have negative c and a. A third possibility is to consider higher-spin conformal f...

On conformal higher spin wave operators

We analyze free conformal higher spin actions and the corresponding wave operators in arbitrary even dimensions and backgrounds. We show that the wave operators do not factorize in general, and identify the Weyl tensor and its derivatives as the obstruction to factorization. We give a manifestly factorized form for them on (A)dS backgrounds for arbitrary spin and on Einstein backgrounds for spi...

Bounding the Partition Function of Spin-Systems

With a graph G = (V,E) we associate a collection of non-negative real weights ⋃ v∈V {λi,v : 1 ≤ i ≤ m} ∪ ⋃ uv∈E{λij,uv : 1 ≤ i ≤ j ≤ m}. We consider the probability distribution on {f : V → {1, . . . ,m}} in which each f occurs with probability proportional to ∏ v∈V λf(v),v ∏ uv∈E λf(u)f(v),uv . Many well-known statistical physics models, including the Ising model with an external field and the...

Zeros of the Partition Function for Higher–Spin 2D Ising Models

We present calculations of the complex-temperature zeros of the partition functions for 2D Ising models on the square lattice with spin s = 1, 3/2, and 2. These give insight into complex-temperature phase diagrams of these models in the thermodynamic limit. Support is adduced for a conjecture that all divergences of the magnetisation occur at endpoints of arcs of zeros protruding into the FM ph...

Spin-Wave theory and Asymptotically Free Beta-Function