Transverse Ising Chain Model

The Ising Chain Model with magnetic fields applied perpendicular to the spin-spin interaction axis.

Hamiltonian

$H=-J{\sum }_{i=1}^{N-1}{\sigma }_i^z{\sigma }_{i+1}^z-h{\sum }_{i=1}^N{\sigma }_i^x$

• $J$: coupling strength between neighboring spins
• $h$: transverse field strength
• ${\sigma }^{x,z}$: Pauli matrices

Key Properties

• Exactly solvable via the Jordan-Wigner transformation
• Exhibits a Quantum Phase Transition at $h/J=1$ (1D case)
• Paradigmatic model for studying symmetry breaking and critical phenomena