In relation to the code below, is the "AccountId" a standard field in the opportunity object? I don't think the last code (acc.Id = opp.AccountId) is valid.
for (Opportunity opp : Trigger.new) {
// Make sure we meet the minimum threshold
if (opp.Amount >= OPP_MIN_VALUE) {
// This is a trick to get the related account
Account acc = new Account();
acc.Id = opp.**AccountId**;