Fixed scale approach to equation of state in lattice QCD

Abstract

A new approach to study the equation of state in finite-temperature QCD is proposed on the lattice. Unlike the conventional method in which the temporal lattice size Nt is fixed, the temperature T is varied by changing Nt at fixed lattice scale. The pressure of the hot QCD plasma is calculated by the integration of the trace anomaly with respect to T at fixed lattice scale. This "T -integral method" is tested in quenched QCD on isotropic and anisotropic lattices and is shown to give reliable results especially at intermediate and low temperatures.

QCD thermodynamics with continuum extrapolated Wilson fermions I

“…the ratio of the kaon decay constant and the pseudoscalar masses: f K /M π and f K /M K ) are called lines of constant physics (LCP). The fixed scale approach of Wilson thermodynamics [14] is in some sense the opposite. One takes a given β to fix the lattice spacing and uses several N t values to scan the temperature.…”

“…As we have seen such results are universal and can be cross-checked with other results obtained by other fermion formalisms, actions etc. For some recent Wilson thermodynamics results see [14][15][16][17][18][19][20].…”

Towards the QCD equation of state at the physical point using Wilson fermion

“…As a possible way out, we have developed the fixed-scale approach, in which the temperature T = (N t a) −1 is varied by varying a temporal lattice size N t at a fixed lattice spacing a [3,4,5]. Because the approach can fix the coupling parameters for all temperatures, zero-temperature simulations to renormalize observables at finite temperatures are common.…”

“…In the fixed-scale approach, the trace anomaly ε −3p is calculated as usual at each temperature, where ε and p are the energy density and the pressure, respectively, To calculate the pressure nonperturbatively, we adopt the 'T -integration method' [3]:…”

Finite-temperature QCD

“…On the left, a test is shown of the new approach of ref. [34], in which the lattice spacing is kept fixed and the temperature is varied through changing the number of points in the Euclidean time direction, N τ ; this is theoretically more transparent than the standard approach where N τ is kept fixed and temperature is varied through β L , implying a simultaneous variation of the lattice spacing. On the right, a very precise study of the entropy density at low temperatures is shown; the entropy density is a convenient observable in that it can be measured without any subtractions (because the entropy density of the vacuum state vanishes), through…”