Universal behaviors of mutual information in one-dimensional <InlineEquation ID="Equ1"> <EquationSource Format="TEX">${\sf J}_1-{\sf J}_2$</EquationSource> </InlineEquation> model

The critical behaviors of the entropy correlation effects in the one dimensional J<Subscript>1</Subscript>-J<Subscript>2</Subscript> Heisenberg model are studied. It is shown that the mutual information or the correlation entropy captures the key features of information about critical fluctuations and can be used to quantify the quantum and finite-temperature phase transitions. At the critical point, the mutual information is power-law decay and the entanglement correlation length is infinite. While far away from the critical point, the mutual information is exponential decay and the entanglement correlation length is finite. A universal property of the mutual information is also found. Based on the critical behaviors of the mutual information, a new method to quantify the infinite order phase transition in the system is proposed. Copyright EDP Sciences/Società Italiana di Fisica/Springer-Verlag 2008