  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.
