The J1–J2 model is a quantum spin model like the Heisenberg model but also includes a term for the interaction between next-nearest neighbor spins.

Hamiltonian

represents the exchange interaction to the next nearest-neighbor.

Where:

• is the list of nearest neighbors

• is the list of next-nearest neighbors

Geometric Frustration

In the study of magnetic systems, the possibility of geometric frustration arises when either the geometry of the lattice model term alone is the Néel State term alone favors a Collinear Striped State in which rows are ferromagnetic along one direction and antiferromagnetically aligned along the other. The competition between these orders drives the physics of the model.

Ground State Phase Diagram

Classical Limit

In the classical limit (where quantum fluctuations are negligible), the ground state undergoes a first-order phase transition, the striped collinear state is stable.

Quantum Case: S = 1/2

, quantum fluctuations alter the phase diagram significantly. The following phases have been established:

• Néel phase): Long-range antiferromagnetic order similar to the Heisenberg model, though with reduced staggered magnetization due to quantum fluctuations.

• Quantum paramagnetic / spin liquid phase): An intermediate region without conventional magnetic long-range order. This is a leading candidate for a quantum spin liquid state, where spins remain dynamically disordered even at zero temperature.

• Collinear striped phase): Magnetic order returns, but with the collinear stripe pattern.

The transition from Néel phase to spin liquid phase is generally believed to be continuous (second-order), while the transition into collinear phase is first-order.

See also

• Spin model

• Heisenberg model (quantum)

• Hubbard model

• t-J model

• Majumdar–Ghosh model

References