Because the response of a magnetic substance to an applied field depen
ds strongly on the physical properties of the material, much can be le
arned by monitoring that response through what is known as a ''magneti
c hysteresis loop''. The measurements are rapid and quickly becoming p
art of the standard set of tools supporting paleomagnetic research. Ye
t the interpretation of hysteresis loops is not simple. It has become
apparent that although classic ''single-domain'', ''pseudo-single-doma
in'' and ''multidomain'' loops described in textbooks occur in natural
samples, loops are frequently distorted, having constricted middles (
wasp-waisted loops) or spreading middles and slouching shoulders (potb
ellies). Such complicated loops are often interpreted in oversimplifie
d ways leading to erroneous conclusions. The physics of the problem ha
ve been understood for nearly half a century, yet numerical simulation
s appropriate to geological materials are almost unavailable. In this
paper we discuss results of numerical simulations using the simplest o
f systems, the single-damain/superparamagnetic (SD/SP) system. Examina
tion of the synthetic hysteresis loops leads to the following observat
ions: (1) Wasp-waisting and potbellies can easily be generated from po
pulations of SD and SP grains. (2) Wasp-waisting requires an SP contri
bution that saturates quickly resulting in a steep initial slope, and
potbellies require low initial slopes (the SP contribution approaching
saturation at higher fields). The approach to saturation is dependent
on volume hence the cube of grain diameter. Therefore there is a very
strong dependence of hysteresis loop shape on the assumed threshold s
ize. (3) We were unable to generate potbellies using a SP/SD threshold
size as large as 30 nm, and wasp waists cannot be generated using a t
hreshold size as small as 8 nm. The occurrence of both potbellies and
wasp waists in natural samples is consistent with a room temperature t
hreshold size of some 15 nm (+/- 5). (4) Simulations using a threshold
size of 15-20 nm with populations dominated by SP grain sizes, that i
s with a small number of SD grains, produce synthetic hysteresis loops
consistent with measured hysteresis loops and transmission electron m
icroscopic observations from submarine basaltic glass. (5) Simulations
and measurements using two populations with distinct coercivity spect
ra can also generate wasp-waisted loops. A relatively straightforward
analysis of the resulting loops can distinguish the latter case from w
asp-waisting resulting from SP/SD behavior.