Random spin-3/2 antiferromagnetic Heisenberg chains revisited

We revisit the spin-reduction transition in the random spin-$3\mathrm{/}2$ antiferromagnetic Heisenberg chain using the tensor-network strong-disorder renormalization group (tSDRG). The predicted transition separates two random-singlet (RS) phases: one formed by effective spin-$1\mathrm{/}2$ moments at weaker disorder and the other by full spin-$3\mathrm{/}2$ moments at stronger disorder. Within the Damle–Huse classification, this transition corresponds to an emergent permutation-symmetric ${\mathcal{P}}_4$ multicritical point on a ${\mathcal{P}}_2$ critical line associated with the RS phases. We first derive the critical exponents governing the disorder-averaged bulk and end-to-end correlation functions in the ${\mathcal{P}}_n$ universality classes within the Damle–Huse framework. Using these theoretical predictions, together with a diagnostic constructed from the mean and variance of the energy-gap distribution, we identify the ${\mathcal{P}}_4$ transition point and the reentrant behavior of the RS phase.