Thermal Entropy and Heat Capacity Anomalies in Low-Dimensional Magnets

Abstract

Low-dimensional magnetic materials frequently display heat capacity anomalies that depart sharply from
conventional three-dimensional long-range-order predictions, but disentangling short-range magnetic correlation
effects from genuine phase-transition signatures in these anomalies requires quantitative entropy accounting that is
not always reported alongside raw heat capacity data. We performed quantum Monte Carlo simulations of the
specific heat and magnetic entropy of spin-1/2 Heisenberg chains and ladders across a temperature range of 0.05
to 20 J/k_B (J the exchange coupling), for chain lengths of 16, 32, 64, and 128 sites and interchain coupling ratios
(J_perp/J) of 0, 0.1, 0.3, and 1.0, using stochastic series expansion sampling with 2 x 10^6 Monte Carlo sweeps per
parameter point after equilibration. The isolated spin chain (J_perp = 0) displayed a broad Schottky-like heat
capacity maximum at T = 0.48 J/k_B with peak value C/Nk_B = 0.350, recovering only 68% of the full magnetic
entropy of R ln(2) per spin by T = 1.0 J/k_B and the remaining 32% only asymptotically at higher temperature,
consistent with persistent short-range antiferromagnetic correlations well above the peak temperature. Introducing
interchain coupling produced a second, sharper low-temperature heat capacity peak signaling the onset of
long-range order, with the ordering temperature T_N rising from undetectable (J_perp = 0) to 0.028 J/k_B at
J_perp/J = 0.1 and 0.19 J/k_B at J_perp/J = 1.0, a roughly seven-fold increase across the tested coupling range,
while the high-temperature Schottky maximum shifted by less than 4% in position across the same range.
Finite-size scaling of the low-temperature peak across chain lengths of 16 to 128 sites showed the peak height
increasing with system size and extrapolating, via a second-order polynomial fit in inverse chain length (R^2 =
0.991), to a thermodynamic-limit ordering signature consistent with three-dimensional universality class
expectations at finite J_perp. The fraction of total magnetic entropy released below the low-temperature ordering
peak, as opposed to the broad short-range-order maximum, increased from below 1% at J_perp/J = 0.1 to 14% at
J_perp/J = 1.0, quantifying how interchain coupling redistributes entropy release between short-range and
long-range-order channels. These results provide a quantitative entropy-partitioning framework for interpreting the
characteristic two-peak heat capacity signature of quasi-one-dimensional magnets and clarify how weak interchain
coupling controls the balance between short-range and long-range magnetic ordering.