/************************************************
*						*
*                  Xrenor			*
*			                   	*
*		Orlando Gonzalez		*
*		orlando@physics.uc.edu		*
*						*
************************************************/

This is an Xwindow program to illustrate the concept of
renormalization group (RG) transformations in real space.
The Monte Carlo configurations in a spin-1/2 Ising model
we use are generated by the program written by Michael Creutz
(creutz@bnl.gov) called 'xising.c'. For details about the 
2-d Ising model simulation and code, please check:

http://thy.phy.bnl.gov/www/xtoys/xtoys.html

I modified the original code and included functions to perform
RG transformations and calculate the magnetization.

To carry out the RG transformations I used the block-spin
transformation: a b x b block of spins is replaced by a
superspin whose state is determined by the state of the
majority of spins in the block, i.e. the majority rule.

The magnetization can be defined as the absolute value of the
number of up spins minus the number of down spins, divided by
the total number of spins.

For details about the renormalization group method you might
read the paper "Problems in Physics with Many Scales of Length",
by Kenneth G. Wilson (Scientific American 241, 158, August 1979).

The program should run on anything supporting Xwindow.
To compile try

cc -O -o xrenor -L/usr/X11R6/lib xrenor.c -lm -lX11

It usually works.  

On Sun workstations the X stuff is in an unconventional place;
try 

gcc -O -o xrenor -I/usr/openwin/include -L/usr/openwin/lib xrenor.c -lm -lX11

Remember, as with any Xwindow program, you need to have "xhost" and
"DISPLAY" set up properly to run it.

The display shows the two dimensional array of spins, each of which
is represented by a bit in a bit map displayed on the screen.  
Black and grey represent the two possible states of a given spin.
The display has a thermometer to indicate the temperature and 
various buttons for controlling the updating, temperature, the
boundary conditions, and the speed. The inverse temperature, beta,
is displayed above the thermometer.

When the "rg" button is pressed for the first time we choose the
initial configuration to start doing the RG transformation
(original lattice or stage 0). Then, by pressing the "rg" button
repeatedly the block-spin transformation is applied, each time 
elucidating the behavior of the system at a larger scale.

There is a limitation on the lattice size, and the program doesn't
work OK when you resize and/or move the windows.