  In this work we extend the notion of what is meant by a meanfield. Meanfields
are approximately maps - through some self consistency relation - of a complex,
usually manybody, problem to a simpler more readily solvable problem. This
mapping can then be solved to represent properties of the complex many body
problem using some self consistency relations. Prototypical examples of simpler
meanfield problems (meanfield systems) are the single site and free particle
problems. Here we propose a new class of simple meanfield systems where the
simple problem to be solved is a 1D spin chain. These meanfields are
particularly useful for studying quasi-1D models, where there is a 3D system
composed of weakly coupled 1D spin chains with the coupling in the transverse
direction weaker than in the 1D direction. We illustrate this idea by
considering meanfields for the Ising (of any coupling sign) and ferromagnetic
Heisenberg models with one direction coupled much more strongly then the other
directions (quasi-1D systems) which map at meanfield level onto the 1D Ising
and 1D ferromagnetic Heisenberg models. We also consider more exotic models to
illustrate other methods of solving 1D systems, namely the $N$-state Potts
model. Magnetic phase transition temperatures and are obtained for all three
models, we see that they significantly differ from the usual meanfield
estimates. Indeed if the 1D direction has coupling $\Gamma$ and the transverse
directions have coupling $J$ with $\lambda\sim\frac{\Gamma}{J}\gg1$ then
regular meanfield would predict the transition temperature to be
$k_{B}T_{c}\sim\Gamma$ for all three models while 1D meanfield predicts
temperatures of $k_{B}T_{c}\sim\frac{\Gamma}{\log\left(\lambda\right)}$ for the
Ising and Potts models and $k_{B}T_{c}\sim\frac{\Gamma}{\sqrt{\lambda}}$ for
the ferromagnetic Heisenberg model. Cluster 1D meanfield extensions are also
proposed.
