Note that there is considerable disagreement as to the exact implementation of minarchism. The real meaning of making government as small as possible is the subject of spirited debate. Many
minarchists, for example dislike and distrust the idea of a standing army. The
Founding Fathers of the
United States of America were one such group, in fact.
Generally speaking, if the government spends money on it, they will find a reason to use it, even if they have to manufacture an excuse. Madeleine Albright, for example, once said something to the effect of what was the use of having this wonderful military, if we weren't going to use it. So some would put a standing army in the category of things which are a threat to freedom. World War I was largely a product of belligerence brought about by competing standing armies.
There is also disagreement as to how the government, minimal as it may be, would be funded. Ayn Rand supported lotteries, but, unless the government was willing to outlaw them for everyone else, it is hard to imagine why the market would choose one from them as opposed to a private lottery, since the payouts from the government lottery would necessarily be less than an equivilently sized private one, since substantial funds would be used for government operational costs. Others support tariffs, which some regard as violations of property rights. Still others support user fees on things such as roads and courts.