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We study the melting of charge order in the half doped manganites using amodel that incorporates double exchange, antiferromagnetic superexchange, andJahn-Teller coupling between electrons and phonons. We primarily use a realspace Monte Carlo technique to study the phase diagram in terms of appliedfield $(h)$ and temperature $(T)$, exploring the melting of charge order withincreasing $h$ and its recovery on decreasing $h$. We observe hysteresis inthis response, and discover that the `field melted' high conductance state canbe spatially inhomogeneous even without extrinsic disorder. The hystereticresponse plays out in the background of field driven equilibrium phaseseparation. Our results, exploring $h$, $T$, and the electronic parameterspace, are backed up by analysis of simpler limiting cases and a Landauframework for the field response. This paper focuses on our results in the`clean' systems, a companion paper studies the effect of cation disorder on themelting phenomena.

A Real Space Description of Magnetic Field Induced Melting in the Charge Ordered Manganites: I. The Clean Limit