Erratum to: Exact Results for One Dimensional Fluids Through Functional Integration

1 Erratum to: J Stat Phys DOI 10.1007/s10955-016-1510-3

In the article “Exact Results for One Dimensional Fluids Through Functional Integration” by Riccardo Fantoni the Eq. (57) of Sect. 8 should read

$$\begin{aligned} C(x_i,x_j)=\frac{2}{\theta \sigma ^2}w(x_i,x_j)= \prod _{k=i}^{j-1}A(|x_{k}-x_{k+1}|), \end{aligned}$$

(1)

with $x_i\le x_{i+1}\le x_{i+2}\le \cdots \le x_j$. So the interaction between particle i and particle j depends on how many particles lie between them. This is a particular non pairwise-additive interaction model. That is, taking $v=A\theta \sigma ^2/4$, the model fluid studied in Sect. 8 and the following subsections is one with a potential energy of the following form

$$\begin{aligned} V_N=\sum _{i<j}\prod _{k=i}^{j-1}v(|x_{k}-x_{k+1}|), \end{aligned}$$

(2)

for a configuration with $x_1\le x_2\le x_3\le \cdots \le x_N$.