Disordered ground states in one-dimensional exactly solvable fluids

RESUMO

One-dimensional fluids of classical hard-core particles of diameter $a$, interacting in pairs via a soft repulsive (monotonically decreasing) potential of finite range $\varphi(x)=\varepsilon \left[ (a'-x)/(a'-a)\right]^{1/\nu}$ $(a\le x\le a')$ with real positive parameters $\varepsilon$ and $\nu$, are studied in an isothermal-isobaric ensemble. If $a'\le 2a$, the pairwise interactions are reduced to nearest-neighbour interactions, which allows for an exact solution of the thermal equilibrium. We focus on the $T\to 0$ 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 $\varphi(x)$ is concave $(\nu\ge 1)$, there exists an ``incompressibility'' pressure $p_i=\varepsilon/(a'-a)$ 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 $\nu>1$ (strict concavity), the ground state at $p=p_i$ is disordered with $l_0=\left[ \nu a +(\nu-1)a'\right]/(2\nu-1)$ and $g_0(x)$ being a superposition of weighted Dirac delta functions over discrete positions. If $\nu=1$ (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 $\varphi(x)$ ($\nu\ge 1$) 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 $p_i$.