We derive exact critical-temperature bounds for the classical ferromagnetic Ising model on two-dimensional periodic tessellations of the plane. For any such tessellation or lattice, the critical temperature is bounded from above by a universal number that is solely determined by the largest coordination number on the lattice. Crucially, these bounds are tight in some cases, such as the honeycomb, square, and triangular lattices. We prove the bounds using the Feynman–Kac–Ward formalism, confirm their validity for a selection of more than 200 lattices, and construct a two-dimensional lattice with 24-coordinated sites and a high critical temperature.

Close

PrevNext

View figure in article

• Magnetic phase transitions
• Transition temperature
• 2-dimensional systems
• Crystal structures
• Lattice models in statistical physics
• Ising model
• Transfer matrix calculations