tikz axis font size
tick label style={font=tiny}
( where tiny can be changed to small, large, etc. )
E.g.
pgfplotsset{every axis/.append style={
axis x line=middle, % put the x axis in the middle
axis y line=middle, % put the y axis in the middle
axis line style={<->}, % arrows on the axis
xlabel={$x$}, % default put x on x-axis
ylabel={$y$}, % default put y on y-axis
label style={font=tiny},
tick label style={font=tiny}
}}