Disordered ground states in one-dimensional exactly solvable fluids
Abstract
One-dimensional fluids of classical hard-core particles of diameter a, interacting in pairs via a soft repulsive (monotonically decreasing) potential of finite range φ(x)=ε [ (a'−x)/(a'−a)]1/ν (a≤ x≤ a') with real positive parameters ε and ν, are studied in an isothermal-isobaric ensemble. If a'≤ 2a, the pairwise interactions are reduced to nearest-neighbour interactions, which allows for an exact solution of the thermal equilibrium. We focus on the T→ 0 ground states, specifically on the equation of state for the mean distance between nearest neighbours l0 and the pair correlation function g0(x). If φ(x) is concave (ν≥ 1), there exists an ``incompressibility'' pressure pi=ε/(a'−a) such that the ground state is an equidistant chain of particles with spacing l0=a' for 0<p<pi and with spacing l0=a for p>pi. If ν>1 (strict concavity), the ground state at p=pi is disordered with l0=[ νa +(ν−1)a']/(2ν−1) and g0(x) being a superposition of weighted Dirac delta functions over discrete positions. If ν=1 (linear ramp), the ground state at p=pi is disordered with l0=(a+a')/2 and the continuous g0(x) is a superposition of Heaviside step functions multiplied by polynomials in x. The isothermal susceptibility at T=0 is nonzero for concave φ(x) (ν≥ 1) at p=pi and, therefore, the corresponding disordered ground states are non-hyperuniform, i.e., they resemble disordered fluids at nonzero temperatures. It turns out that pair correlation functions of disordered ground states, which occur only at a single pressure pi, extend their predictive power to thermodynamic states at nonzero temperatures over a wider range of pressures around pi.
Versions
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BibTeX
@misc{travenec2026disordered,
title = {{Disordered ground states in one-dimensional exactly solvable fluids}},
author = {Igor Travěnec and Ladislav Šamaj},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.11394},
eprint = {2609.11394},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.11394},
}
RIS
TY - UNPB
TI - Disordered ground states in one-dimensional exactly solvable fluids
AU - Igor Travěnec
AU - Ladislav Šamaj
PY - 2026
DA - 2026/09/10
PB - arXiv
DO - 10.48550/arxiv.2609.11394
UR - https://arxiv.org/abs/2609.11394
AB - One-dimensional fluids of classical hard-core particles of diameter a, interacting in pairs via a soft repulsive (monotonically decreasing) potential of finite range φ(x)=ε [ (a'−x)/(a'−a)]^1/ν (a≤ x≤ a') with real positive parameters ε and ν, are studied in an isothermal-isobaric ensemble. If a'≤ 2a, the pairwise interactions are reduced to nearest-neighbour interactions, which allows for an exact solution of the thermal equilibrium. We focus on the T→ 0 ground states, specifically on the equation of state for the mean distance between nearest neighbours l_0 and the pair correlation function g_0(x). If φ(x) is concave (ν≥ 1), there exists an ``incompressibility'' pressure p_i=ε/(a'−a) such that the ground state is an equidistant chain of particles with spacing l_0=a' for 0<p<p_i and with spacing l_0=a for p>p_i. If ν>1 (strict concavity), the ground state at p=p_i is disordered with l_0=[ νa +(ν−1)a']/(2ν−1) and g_0(x) being a superposition of weighted Dirac delta functions over discrete positions. If ν=1 (linear ramp), the ground state at p=p_i is disordered with l_0=(a+a')/2 and the continuous g_0(x) is a superposition of Heaviside step functions multiplied by polynomials in x. The isothermal susceptibility at T=0 is nonzero for concave φ(x) (ν≥ 1) at p=p_i and, therefore, the corresponding disordered ground states are non-hyperuniform, i.e., they resemble disordered fluids at nonzero temperatures. It turns out that pair correlation functions of disordered ground states, which occur only at a single pressure p_i, extend their predictive power to thermodynamic states at nonzero temperatures over a wider range of pressures around p_i.
ER -