Shiyue Ren | Searcharxiv

arXiv2026

An edge-bicolored graph approach to the Ising model on random regular graphs

We give an exact solution of the ferromagnetic Ising model on a random regular graph ensemble via analytic combinatorics. Expressing the partition function as the generating function of labeled edge-bicolored graphs, we obtain the free energy in the thermodynamic limit from the asymptotic enumeration of these graphs. A simple analysis of the resulting formula reveals a second-order phase transition with critical exponents of the mean-field universality class.

math-ph↗

arXiv2025

Tracing the Trace Anomaly of Dense Matter inside Neutron Stars

The trace anomaly $\Delta$ is an important quantity that measures the broken conformal symmetry in neutron star matter. In this work, we present quasi-universal relations that connect the stellar profile of $\Delta$ to the compactness, moment of inertia, and tidal deformability of neutron stars. We apply the quasi-universal relations to determine the trace anomaly profiles for PSR J0030+0451 and PSR J0740+6620 based on their mass-radius measurements. We also analyze PSR J0737-3039A according to its moment of inertia inferred from Bayesian modeling of nuclear equation of state. A recent multimessenger constraint on the tidal deformability is also studied, resulting in an estimate value of the trace anomaly $\Delta_c = 0.1770^{+0.0365}_{-0.0432}$ at the center of a $1.4M_\odot$ canonical neutron star. It is expected that more precise observations from both electromagnetic and gravitational-wave channels in the future will provide tighter constraints on the behavior of $\Delta$ inside neutron stars.

astro-ph.HE↗