Tarnawski, Maciej2015-06-242015-06-241985http://hdl.handle.net/10919/53610We present a method of constructing the phase diagram at low temperatures, using the low temperature expansions. We consider spin Iattice systems described by a Hamiltonian with a d-dimensional perturbation space. We prove that there is a one-one correspondence between subsets of the phase diagram and extremal elements of some family of convex sets. We also solve a linear programming problem of the phase diagram for a set of affine functionals.viii, 111 leavesapplication/pdfen-USIn CopyrightLD5655.V856 1985.T326Phase diagramsStatistical physics -- MathematicsLattice theoryHamiltonian systemsDissertation