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Motivated by the experimental report of unusual low temperature magnetism inquasi one-dimensional magnet CuInVO$_5$, we present results of a clustermean-field study on a spin-$1/2$ Heisenberg model with alternatingferromagnetic and antiferromagnetic nearest-neighbor coupling. We map out theground state phase diagrams with varying model parameters, including the effectof an external magnetic field. An unexpected competition between differentspin-spin correlations is uncovered. Multiple spin-flop transitions areidentified with the help of component resolved correlation functions. For thematerial-specific choice of model parameters we discuss the temperaturedependence of specific heat and magnetic susceptibility, and compare ourresults with the available experimental data. A detailed account of spin-spincorrelations allows us to present a microscopic understanding of thelow-temperature magnetic ordering in CuInVO$_5$. Most notably, we identify theorigin of an extra peak in the low temperature specific heat data of CuInVO$_5$reported by Hase {\it et al.}

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