Critical Dimension and Negative Specific Heat in One-dimensional Large-N Reduced Models

Understand

We investigate critical phenomena of the Yang-Mills (YM) type one-dimensional matrix model that is a large-$N$ reduction (or dimensional reduction) of the $D+1$ dimensional $U(N)$ pure YM theory (bosonic BFSS model).

• This model shows a large-$N$ phase transition at finite temperature, which is analogous to the confinement/deconfinement transition of the original YM theory.
• We study the matrix model at a three-loop calculation via the "principle of minimum sensitivity" and find that there is a critical dimension $D=35.5$: At $D \le 35$, the transition is of first order, while it is of second order at $D\ge 36$.
• Furthermore, we evaluate several observables in our method, and they nicely reproduce the existing Monte Carlo results.