Strong coupling expansion for Yang-Mills theory at finite temperature
Euclidean strong coupling expansion of the partition function is applied tolattice Yang-Mills theory at finite temperature, i.e. for lattices with acompactified temporal direction. The expansions have a finite radius ofconvergence and thus are valid only for $\beta<\beta_c$, where $\beta_c$denotes the nearest singularity of the free energy on the real axis. Theaccessible temperature range is thus the confined regime up to thedeconfinement transition. We have calculated the first few orders of theseexpansions of the free energy density as well as the screening masses for thegauge groups SU(2) and SU(3). The resulting free energy series can be summed upand corresponds to a glueball gas of the lowest mass glueballs up to thecalculated order. Our result can be used to fix the lower integration constantfor Monte Carlo calculations of the thermodynamic pressure via the integralmethod, and shows from first principles that in the confined phase thisconstant is indeed exponentially small. Similarly, our results also explain theweak temperature dependence of glueball screening masses below $T_c$, asobserved in Monte Carlo simulations. Possibilities and difficulties inextracting $\beta_c$ from the series are discussed.