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Heat-capacity measurements are a useful tool for understanding the complexphase behaviour of systems containing one-dimensional motifs. Here we study thesignature within such measurements of the incorporation of defects intoquasi-one-dimensional (q-1D) systems. Using Monte Carlo simulations, we showthat, on dilution by non-interacting sites, q-1D Ising models display alow-temperature signature not present in conventional three-dimensional models.Frustrated embeddings of 1D chains show similar features to unfrustratedembeddings, with the additional emergence of a finite ground-state entropy inthe former, which arises from chain segmentation. We introduce a mean-fieldformulation which captures the low-temperature behaviour of the model. Thistheoretical framework is applied to the interpretation of experimentalheat-capacity measurements of the Tb$_{1-\rho}$Y$_{\rho}$(HCOO)$_3$ family ofmagnetocalorics. We find good correspondence between simulation and experiment,establishing this system as a canonical example of dilute q-1D magnets.

Thermodynamic signatures of chain segmentation in dilute quasi-one dimensional Ising systems