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Quantum magnetism studies collective magnetic behavior in which quantum spin states, noncommuting observables and quantum fluctuations matter. A lattice of local spins can be modeled by a Heisenberg model, whose exchange interaction favors particular relations between neighbours. Its states need not resemble a set of classical arrows pointing in definite directions.

A two-spin spin singlet state illustrates the difference: it has zero total spin while retaining nontrivial spin correlations, rather than two independently known opposite arrows. Large ordered magnets can support spin waves, whereas strong quantum fluctuations can invalidate an expansion around a chosen ordered state. Measurements of magnetic susceptibility, heat capacity and excitation spectra probe different aspects of the same interacting system. The subject is therefore about both collective order and correlated states that resist a simple ordered reference picture.