We investigate nuclear matter on a cubic lattice. An exact thermal formalism is applied to nucleons with a Hamiltonian that accommodates on-site and next-neighbor parts of the central, spin- and isospin-exchange interactions. We describe the nuclear matter Monte Carlo methods which contain elements from shell model Monte Carlo methods and from numerical simulations of the Hubbard model. We show that energy and basic saturation properties of nuclear matter can be reproduced. Evidence of a first-order phase transition from an uncorrelated Fermi gas to a clustered system is observed by computing mechanical and thermodynamical quantities such as compressibility, heat capacity, entropy and grand potential. We compare symmetry energy and first sound velocities with literature and find reasonable agreement.

23 pages, 8 figures (some in color), to be submitted to Phys. Rev. C