Cluster mean field study of the Heisenberg model for CuInVO$_5$

Motivated by the experimental report of unusual low temperature magnetism in quasi one-dimensional magnet CuInVO$_5$, we present results of a cluster mean-field study on a spin-$1/2$ Heisenberg model with alternating ferromagnetic and antiferromagnetic nearest-neighbor coupling. We map out the ground state phase diagrams with varying model parameters, including the effect of an external magnetic field. An unexpected competition between different spin-spin correlations is uncovered. Multiple spin-flop transitions are identified with the help of component resolved correlation functions. For the material-specific choice of model parameters we discuss the temperature dependence of specific heat and magnetic susceptibility, and compare our results with the available experimental data. A detailed account of spin-spin correlations allows us to present a microscopic understanding of the low-temperature magnetic ordering in CuInVO$_5$. Most notably, we identify the origin of an extra peak in the low temperature specific heat data of CuInVO$_5$ reported by Hase {\it et al.}