  Period-colour (PC) and amplitude-colour (AC) relations are studied for the
Large Magellanic Cloud (LMC) Cepheids under the theoretical framework of the
hydrogen ionization front (HIF) - photosphere interaction. LMC models are
constructed with pulsation codes that include turbulent convection, and the
properties of these models are studied at maximum, mean and minimum light. As
with Galactic models, at maximum light the photosphere is located next to the
HIF for the LMC models. However very different behavior is found at minimum
light. The long period (P>10days) LMC models imply that the photosphere is
disengaged from the HIF at minimum light, similar to the Galactic models, but
there are some indications that the photosphere is located near the HIF for the
short period (P<10 days) LMC models. We also use the updated LMC data to derive
empirical PC and AC relations at these phases. Our numerical models are broadly
consistent with our theory and the observed data, though we discuss some
caveats in the paper. We apply the idea of the HIF-photosphere interaction to
explain recent suggestions that the LMC period-luminosity (PL) and PC relations
are non-linear with a break at a period close to 10 days. Our empirical PC and
PL relations are also found to be non-linear with the F-test. Our explanation
relies on the properties of the Saha ionization equation, the HIF-photosphere
interaction and the way this interaction changes with the phase of pulsation
and metallicity to produce the observed changes in the Cepheid PC and PL
relations.
