We study the universal properties of near-threshold $s$ -wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness. Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems. When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates. In contrast, in the strong-Coulomb regime, this remnant disappears.We study the universal properties of near-threshold $s$-wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness. Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems. When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates. In contrast, in the strong-Coulomb regime, this remnant disappears.

arXiv:2610.08340Oct 6, 20260 citations

Long-range interactions

Dennis C. Rapaport

Cambridge University Press eBooksApr 1, 20042 citations

Direct interaction

Willy Haeberli

Springer eBooksNov 19, 20050 citations

Critical temperature and correlation length of an elastic interaction model for spin-crossover materials

Taro Nakada, Takashi Mori, Seiji Miyashita +4 more

It has previously been pointed out that the coexistence of infinite-range and short-range interactions causes a system to have a phase transition of the mean-field universality class, in which the cluster size is finite even at the critical point. In the present paper, we study this property in a model of bistable molecules, whose size changes depending on the bistable states. The molecules can move in space, interacting via an elastic interaction. It is known that due to the different sizes, an effective long-range interaction between the spins appears, and thus this model has a mean-field type of phase transition. It is found that the scaling properties of the shift of the critical temperature from the pure short-range limit in the model with infinite-range and short-range interactions hold also in the present model, regarding the ratio of the size of the two states as a control parameter for the strength of the long-range interaction. By studying the structure factor, it is shown that the dependence of the cluster size at the critical temperature also shows the same scaling properties as a previously studied model with both infinite-range and short-range interactions. We therefore conclude that these scaling relations hold universally in hybrid models with both short-range and weak long-range interactions.It has previously been pointed out that the coexistence of infinite-range and short-range interactions causes a system to have a phase transition of the mean-field universality class, in which the cluster size is finite even at the critical point. In the present paper, we study this property in a model of bistable molecules, whose size changes depending on the bistable states. The molecules can move in space, interacting via an elastic interaction. It is known that due to the different sizes, an effective long-range interaction between the spins appears, and thus this model has a mean-field type of phase transition. It is found that the scaling properties of the shift of the critical temperature from the pure short-range limit in the model with infinite-range and short-range interactions hold also in the present model, regarding the ratio of the size of the two states as a control parameter for the strength of the long-range interaction. By studying the structure factor, it is shown that the dependence of the cluster size at the critical temperature also shows the same scaling properties as a previously studied model with both infinite-range and short-range interactions. We therefore conclude that these scaling relations hold universally in hybrid models with both short-range and weak long-range interactions.

arXiv:1110.6257Physical Review BFeb 7, 201237 citations

Linear Interactions

WORLD SCIENTIFIC eBooksAug 13, 20170 citations

Crossover between short- and long-range interactions in the one-dimensional Ising model

V.B. Kislinsky, Vyacheslav I. Yukalov

The authors consider the one-dimensional Ising model which besides the interaction of nearest neighbours includes a long-range term. The latter is ferromagnetic while the nearest-neighbour interaction can have any sign. The crossover between short- and long-range interactions when varying the Hamiltonian parameters is analysed for such a model. For some values of the antiferromagnetic short-range interaction the transition from a ferro- to paramagnetic state is of first order. At the tricritical point where the transition order changes from second to first they obtain classical tricritical exponents. For a ferromagnetic short-range interaction the Curie temperature surpasses the transition temperature of the long-range model.The authors consider the one-dimensional Ising model which besides the interaction of nearest neighbours includes a long-range term. The latter is ferromagnetic while the nearest-neighbour interaction can have any sign. The crossover between short- and long-range interactions when varying the Hamiltonian parameters is analysed for such a model. For some values of the antiferromagnetic short-range interaction the transition from a ferro- to paramagnetic state is of first order. At the tricritical point where the transition order changes from second to first they obtain classical tricritical exponents. For a ferromagnetic short-range interaction the Curie temperature surpasses the transition temperature of the long-range model.

Journal of Physics A Mathematical and GeneralJan 7, 19888 citations

We study the universal properties of near-threshold

s

-wave eigenstates in systems with Coulomb plus short-range interactions by analyzing their compositeness. Using a nonrelativistic effective field theory, we derive a relation between the compositeness of near-threshold states and the Coulomb scattering length, the Coulomb effective range, and the Bohr radius. We find that the long-range Coulomb interaction modifies the threshold behavior expected from the low-energy universality of purely short-range systems. When the Coulomb interaction is relatively weak compared with the short-range interaction, a remnant of the low-energy universality associated with the short-range interaction survives, leading to composite-dominant near-threshold eigenstates. In contrast, in the strong-Coulomb regime, this remnant disappears.