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.

In this model, the term ${\displaystyle J_{1}}$ represents the usual nearest-neighbor interaction as seen in the Heisenberg model, and ${\displaystyle J_{2}}$ represents the exchange interaction to the next nearest-neighbor.

Where:

In the study of magnetic systems, the possibility of geometric frustration arises when either the geometry of the lattice model or competing interactions prevent the spin from adopting a simple ordered arrangement which minimizes all bond energies simultaneously. When both ${\displaystyle J_{1}>0}$ and ${\displaystyle J_{2}>0}$ the two interactions are frustrated. The ground state of the ${\displaystyle J_{1}}$ term alone is the Néel State which is a checkerboard of opposing spins while the ${\displaystyle J_{2}}$ 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.

In the classical limit (where quantum fluctuations are negligible), the ground state undergoes a first-order phase transition at the critical ratio ${\displaystyle J_{2}/J_{1}=0.5}$. For ${\displaystyle J_{2}/J_{1}<0.5}$, the Néel state is stable; for ${\displaystyle J_{2}/J_{1}>0.5}$, the striped collinear state is stable.

For quantum spins, particularly ${\displaystyle S=1/2}$, quantum fluctuations alter the phase diagram significantly. The following phases have been established:

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.