Magnetization process of the S = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice

We study the S = 1/2 Heisenberg antiferromagnet on the floret pentagonal lattice by numerical diagonalization method. This system shows various behaviours that are different from that of the Cairo-pentagonal-lattice antiferromagnet. The ground-state energy without magnetic field and the magnetization process of this system are reported. Magnetization plateaux appear at one-ninth height of the saturation magnetization, at one-third height, and at seven-ninth height. The magnetization plateaux at one-third and seven-ninth heights come from interactions linking the sixfold-coordinated spin sites. A magnetization jump appears from the plateau at one-ninth height to the plateau at one-third height. Another magnetization jump is observed between the heights corresponding to the one-third and seven-ninth plateaux; however the jump is away from the two plateaux, namely, the jump is not accompanied with any magnetization plateaux. The jump is a peculiar phenomenon that has not been reported.

Site-Monotonicity Properties for Reflection Positive Measures with Applications to Quantum Spin Systems

We consider a general statistical mechanics model on a product of local spaces and prove that, if the corresponding measure is reflection positive, then several site-monotonicity properties for the two-point function hold. As an application, we derive site-monotonicity properties for the spin–spin correlation of the quantum Heisenberg antiferromagnet and XY model, we prove that spin-spin correlations are point-wise uniformly positive on vertices with all odd coordinates—improving previous positivity results which hold for the Cesàro sum. We also derive site-monotonicity properties for the probability that a loop connects two vertices in various random loop models, including the loop representation of the spin O(N) model, the double-dimer model, the loop O(N) model and lattice permutations, thus extending the previous results of Lees and Taggi (2019).