Hamiltonian systems complex behaviors

The invention of digital computers ushered in a new era of computational methods that numerically determine the partition function, rendering feasible the connection between microscopic Hamiltonians and thermodynamic behavior for complex systems. 

The free energy of a Ginzburg-Landau field describing a system of weakly coupled chains in a plane is identified with the ground-state energy of a linear array of quantum anharmonic oscillators. The equivalent Hamiltonian is simplified for both the real and complex fields using a truncated basis of states. Results for both the real and complex fields will be discussed. In addition, the behavior of the specific heat and inverse correlation length for finite numbers of weakly coupled chains will be discussed. 

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