At low temperatures and high baryon density, the equation of state of dense matter cannot be directly computed from quantum chromodynamics due to the fermion sign problem. Therefore, effective models that incorporate QCD symmetries and reproduce known constraints are used. In such an approach, three conserved charges must be considered: baryon number, strangeness, and electric charge, leading to a three-dimensional space of chemical potentials. This work sits at the intersection of research on quark matter, kilonovae, and magnetars; neighboring studies explore color superconductivity, phase transitions in neutron stars, and quantum critical points. This paper stands out by being the first to demonstrate, within a unified model with the full baryon octet, decuplet, and quarks, the coexistence of three critical points.
The chiral mean-field model CMF++ was used, an open-source version developed by the MUSES collaboration. The model includes chiral symmetry, the full baryon octet, decuplet, and quarks. The equation of state is computed in a four-dimensional parameter space: temperature, baryon, strange, and electric chemical potentials. Positive definiteness of the Hessian matrix is used to identify stable, metastable, and unstable solutions. Phase transitions are identified by discontinuities in thermodynamic quantities, and critical points by peaks in the normalized baryon susceptibility. Calculations were performed for a specific set of coupling constants C3.
At zero temperature, three phases are found: a light hadronic phase (mostly nucleons), a quark phase, and a strangeness-dominated phase (mostly Ξ-, Σ-hyperons and their resonances). The transition to the strange phase is accompanied by a sharp change in composition: the strangeness fraction $Y_S$ ≈ −1, and the isospin asymmetry $δ_I$ drops below 0.25. At finite temperature, each first-order transition ends in a critical point. For the strange transition, the critical temperature $T_c$ ≈ 40 MeV and baryon chemical potential $μ_{Bc}$ ≈ 1345 MeV. The deconfinement line bends toward lower $μ_B$ at low temperatures, opposite to standard behavior. The liquid-gas transition is independent of the presence of the strange critical point.
This work shows that dense nuclear matter may host a third type of phase transition, one dominated by strangeness, which had not been observed in this context before. Unlike neighboring studies where hyperonic instabilities were considered in isolation or within simpler models, here they emerge in a unified, self-consistent model with quarks and the full octet. This is the first demonstration of three critical points in a single CMF phase diagram. The result is important for understanding the composition of neutron star interiors and the dynamics of their mergers.
The stability of the strange phase must be checked for a wider range of CMF parametrizations, since its existence strongly depends on the coupling constants. An open question is how the interaction between the strange transition and deconfinement affects trajectories in chemical potential space under realistic conditions in heavy-ion collisions and neutron star mergers. Plans include investigating the possibility of the strange phase appearing in low-energy collisions.
The results could affect the interpretation of heavy-ion collision data and the modeling of neutron star mergers, including gravitational wave calculations.
Conduct a stability analysis of the strange phase for different CMF parametrizations and study its manifestations in numerical simulations of neutron star mergers, accounting for deviations from electroweak equilibrium.
This work is directly related to the unresolved problem of the equation of state of superdense nuclear matter and the question of which degrees of freedom (hadrons, hyperons, quarks) are realized in neutron star cores. The existence of a strange phase could resolve the contradiction between the softness of the equation of state due to hyperons and the observed masses of neutron stars around two solar masses.
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What the work does
The paper presents the phase diagram of dense nuclear matter within the chiral mean-field model CMF++, which includes the full baryon octet, decuplet, and quarks. Three first-order phase transitions are calculated, each ending in a critical point, including a new transition to a phase dominated by hyperons and resonances at T≈40 MeV and μB≈1345 MeV.
Where its strength is
For the first time, the coexistence of three critical points is demonstrated in a single self-consistent model with quarks and the full baryon spectrum, opening the possibility for a unified description of different regimes of dense matter.
Where it could go next
Worth trying
Why this may matter
If the proposed picture with three critical points is confirmed in a broader class of models, it could provide new benchmarks for heavy-ion collision experiments and for interpreting observational data from neutron star mergers, where dense matter with hyperons may play a significant role.
Nearby works in our archive
The archive is sparse around this work: the closest review is only 0.57, against a usual 0.64. It looks like few have drilled nearby.
The critical temperature of the strange transition, about 40 MeV, corresponds to roughly 460 billion kelvin, which is tens of thousands of times hotter than the center of the Sun.
In Bruce Sterling's novel Schismatrix, intelligent beings are described living in the extreme conditions of neutron stars. Phase transitions like those considered here could define the boundaries of their world.