Griffiths effects in random Heisenberg antiferromagneticS=1chains

Griffiths-McCoy singularities in random quantum spin chains: Exact results

We consider random quantum (tight-binding, XX and Ising) spin chains in the off-critical region and study their Griffiths-McCoy singularities. These are obtained from the density of states of the low-energy excitations, which is calculated exactly by the Dyson-Schmidt method. In large finite systems the low-energy excitations are shown to follow the statistics of extremes and their distribution...

Griffiths effects of the susceptible-infected-susceptible epidemic model on random power-law networks.

We provide numerical evidence for slow dynamics of the susceptible-infected-susceptible model evolving on finite-size random networks with power-law degree distributions. Extensive simulations were done by averaging the activity density over many realizations of networks. We investigated the effects of outliers in both highly fluctuating (natural cutoff) and nonfluctuating (hard cutoff) most co...

Heisenberg Model, Bethe Ansatz, and Random Walks

Random Walk Representations of the Heisenberg Model

In this paper we develop some random walk representations for the spin-S Heisenberg ferromagnet with nearest neighbor interaction on the integer lattice in d dimensions. The representations parallel corresponding representations for the perfect Bose gas. Hence the Heisenberg model can be thought of as an interacting Bose gas. This has been made more explicit in the paper of Dyson (5/ (see also ...

Spin reduction transition in spin - 32 random Heisenberg chains

Random spin3 2 antiferromagnetic Heisenberg chains are investigated using an asymptotically exact renormalization group. Randomness is found to induce a quantum phase transition between two random-singlet phases. In the strong randomness phase the effective spins at low energies are Se f f5 3 2 , while in the weak randomness phase the effective spins are Se f f5 1 2 . Separating them is a quant...