Mappings of classical computation onto statistical mechanics models have led to remarkable successes in addressing some complex computational problems. However, such mappings display thermodynamic phase transitions that may prevent reaching solution even for easy problems known to be solvable in polynomial time. Here we map universal reversible classical computations onto a planar vertex model ...

The ground state energy and energy gap to the first excited state are calculated for the attractive Hubbard model in one dimension using both the Bethe Ansatz equations and the variational BCS wavefunction. Comparisons are provided as a function of coupling strength and electron density. While the ground state energies are always in very good agreement, the BCS energy gap is sometimes incorrect...

Neodyme spherical magnets are inexpensive objects that demonstrate how dipolar particles self-assemble into various structures ranging from 1D chains to 3D crystals. The dipole-dipole interactions confer the stability these particular architectures. In present paper, we explore ordered only, and evidence hybrid magnetocrystals, alternating hexagonal planes of antiparallel dipoles, have lowest m...