Numerical study of the Nambu-Goto string model at finite length and temperature

We study the Nambu-Goto model numerically for a string of finite length at an arbitrary temperature. The static quark-antiquark potential is investigated and it is found that the deconfinement radius rdec (the distance between quarks for which the potential vanishes) is independent of the temperature. For {τ}=τdec (the temperature for which the string tension vanishes), the potential becomes a constant for large r, thus losing its ``confining'' property. This is clearly a consistent result with the interpretation of τdec as a deconfinement temperature. For {τ}>τdec, solutions to the gap equations exist which allow us to have a well-defined quark potential although only for ``unconfining'' strings of a certain length. The string tension at finite temperature for a string of various lengths is also calculated as well as τdecᵐᵃˣ (the maximum temperature for which a tension exists) which might signal a first-order transition to a deconfined phase.