## Lines of Constant Physics.

##### Abstract

To investigate the properties of the proton at finite temperature, a Monte-Carlo simulation of a skyrmion on a four dimensional lattice is run. From these runs two dimensionless quantities related to the mass and radius are calculated, m =M a and r =R/ a , respectively, where a is the lattice spacing. The goal is to find the functions M(T) and R(T), which give the mass and size of the proton for different temperatures. To do this, m and r are calculated for multiple values of the couplings b 1 and b 2 at T=0. The two functions, m and r , are then multiplied together and plotted with respect to b 1 and b 2, producing a two-dimensional surface. From this surface, it is possible to extract a line along which mr =constant. This is called the line of constant physics (LCP) because all physics along this curve is the same. For a proton, mr =2.5. With the LCP, together with M=1GeV for a proton, we can determine the lattice spacing, a , for any value of b 1 and b 2. Also, since a is inversely proportional to temperature, knowledge of the LCP allows one to calculate M(T) and R(T) for any finite temperature.