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 ${\mathit{r}}_{\mathrm{dec}}$ (the distance between quarks for which the potential vanishes) is independent of the temperature. For τ=${\mathrm{\tau }}_{\mathrm{dec}}$ (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 ${\mathrm{\tau }}_{\mathrm{dec}}$ as a deconfinement temperature. For τ>${\mathrm{\tau }}_{\mathrm{dec}}$, 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 ${\mathrm{\tau }}_{\mathrm{dec}}^{\max }$ (the maximum temperature for which a tension exists) which might signal a first-order transition to a deconfined phase.