The nature of the phase transitions in La$_{1-x}$Ca$_x$MnO$_3$ and Pr$_{0.48}$Ca$_{0.52}$MnO$_3$ has been probed using heat capacity and magnetisation measurements. The phase transition associated with the onset of the stripe phase has been identified as second order. The model of a Peierls transition in a disordered system (a `dirty Peierls transition) is shown to provide an extremely good fit to this transition. In addition, an unexpected magnetic phase has been revealed in low temperature Pr$_{0.48}$Ca$_{0.52}$MnO$_3$, associated with an excess heat capacity over a wide temperature range compared to La$_{1-x}$Ca$_x$MnO$_3$.
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