2023/06/12 by Sanwari, Riekshika, Khatua, Soumen, Sahay, Anurag
#FOS: Physical sciences #Materials Science (cond-mat.mtrl-sci) #Statistical Mechanics (cond-mat.stat-mech)
paper · doi:10.48550/arxiv.2306.06876
Four-dimensional state space geometry is worked out for the exactly solved one-dimensional spin-3/2 lattice with a Blume-Emery-Griffiths (BEG) Hamiltonian as well as a more general one with a term containing a non-zero field coupling to the octopole moments. The phase behaviour of the spin-3/2 chain is also explored extensively and novel phenomena suggesting anomalies in the hyperscaling relation and in the decay of fluctuations are reported for a range of parameter values. Using the method of constrained fluctuations worked out earlier in \citeasknbads,riekan1 three sectional curvatures and a 3d curvature are obtained and shown to separately encode dipolar, quadrupolar and octopolar correlations both near and away from pseudo-criticality. In all instances of a seeming hyperscaling violation the 3d scalar curvature is found to encode the correlation length while the relevant 2d curvature equals the inverse of singular free energy. For parameter values where the order parameter fluctuation anomalously decays despite a divergence in correlation length the relevant scalar curvature undergoes a sign change to positive values, signalling a possible change in statistics.