Thermodynamics of strongly interacting plasma with high accuracy

The equation of state of $SU(3)$ Yang-Mills theory is investigated in the framework of a moving reference frame. Results for the entropy density, the pressure, the energy density, and the trace anomaly are presented for temperatures ranging from 0 to 230 $T_c$, with $T_c$ the deconfinement temperature. The entropy density is the primary observable that has been measured and form which the other thermodynamic quantities are obtained. At least 4 different values of the lattice spacing have been considered at each physical temperature in order to extrapolate to the continuum limit. The final accuracy is 0.5%, increasing to about 1% close to the phase transition. A detailed comparison with the results available in the literature is discussed.Comment: Proceedings of the 34th International Symposium on Lattice Field Theory - 24-30 July 2016 - Southampton, UK. PoS (LATTICE2016) 06

Equation of state of the SU(33) Yang-Mills theory: a precise determination from a moving frame

The equation of state of the SU($3$) Yang-Mills theory is determined in the deconfined phase with a precision of about 0.5%. The calculation is carried out by numerical simulations of lattice gauge theory with shifted boundary conditions in the time direction. At each given temperature, up to $230\, T_c$ with $T_c$ being the critical temperature, the entropy density is computed at several lattice spacings so to be able to extrapolate the results to the continuum limit with confidence. Taken at face value, above a few $T_c$ the results exhibit a striking linear behaviour in $\ln(T/T_c)^{-1}$ over almost 2 orders of magnitude. Within errors, data point straight to the Stefan-Boltzmann value but with a slope grossly different from the leading-order perturbative prediction. The pressure is determined by integrating the entropy in the temperature, while the energy density is extracted from $T s=(\epsilon + p )$. The continuum values of the potentials are well represented by Pad\'e interpolating formulas, which also connect them well to the Stefan-Boltzmann values in the infinite temperature limit. The pressure, the energy and the entropy densities are compared with results in the literature. The discrepancy among previous computations near $T_c$ is analyzed and resolved thanks to the high precision achieved.Comment: 7 pages, 3 figures. A few sentences and one reference adde

Non-trivial \theta-Vacuum Effects in the 2-d O(3) Model

We study \theta-vacua in the 2-d lattice O(3) model using the standard action and an optimized constraint action with very small cut-off effects, combined with the geometric topological charge. Remarkably, dislocation lattice artifacts do not spoil the non-trivial continuum limit at \theta\ non-zero, and there are different continuum theories for each value of \theta. A very precise Monte Carlo study of the step scaling function indirectly confirms the exact S-matrix of the 2-d O(3) model at \theta = \pi.Comment: 4 pages, 3 figure

Study of theta-Vacua in the 2-d O(3) Model

We investigate the continuum limit of the step scaling function in the 2-d O(3) model with different theta-vacua. Since we find a different continuum value of the step scaling function for each value of theta, we can conclude that theta indeed is a relevant parameter of the theory and does not get renormalized non-perturbatively. Furthermore, we confirm the result of the conjectured exact S-matrix theory, which predicts the continuum value at theta = pi. To obtain high precision data, we use a modified Hasenbusch improved estimator and an action with an optimized constraint, which has very small cut-off effects. The optimized constraint action combines the standard action of the 2-d O(3) model with a topological action. The topological action constrains the angle between neighboring spins and is therefore invariant against small deformations of the field.Comment: 7 pages, 4 figures, The 30 International Symposium on Lattice Field Theory - Lattice 2012, June 24-29, 2012, Cairns, Australi