If a neighbor calls the police and says I'm doing drugs in my house/yard and I'm inside by the time the police get there, do they have probable cause to search my property?
It depends on the actual content of the tip and to what degree the police believe the tip to be reliable given the totality of the circumstances. I'll give two examples where tips (one actually anonymous, one deemed anonymous) were found to give probable cause or reasonable suspicion to support a search or seizure.
Illinois v Gates 462 U.S. 213 (1983) established that the test for whether there is probable cause for issuance of a warrant is based on the "totality of the circumstances".
In Gates, police received an anonymous letter disclosing that the defendant was selling drugs, along with some predictions about the defendant's future activity. After verifying that some of the predictions were correct, the police obtained a search warrant for the home.
The court observed that "under the "totality of the circumstances" analysis, corroboration of details of an informant's tip by independent police work is of significant value."
Navarette v California 572 U.S. ___ (2014) reiterated that "reasonable suspicion takes into account the totality of the circumstances, and depends upon both the content of information possessed by police and its degree of reliability. An anonymous tip alone seldom demonstrates sufficient reliability, but may do so under appropriate circumstances" (quoting from the syllabus, with internal citations and quotations removed).
In Navarette, an 911 caller asserted that a truck with a particular appearance was driving erratically and had run her off the road.
The court said: "Even assuming for present purposes that the 911 call was anonymous, we conclude that the call bore adequate indicia of reliability for the officer to credit the caller’s account. The officer was therefore justified in proceeding from the premise that the truck had, in fact, caused the caller’s car to be dangerously diverted from the highway."
They also observed that "a 911 call has some features that allow for identifying and tracing callers, and thus provide some safeguards against making false reports with immunity."
Probable cause is defined as: "a reasonable amount of suspicion, supported by circumstances sufficiently strong to justify a prudent and cautious person's belief that certain facts are probably true" (See Wikipedia citing Handler, J. G. (1994). Ballentine's Law Dictionary (Legal Assistant ed.). Albany: Delmar. p. 431.)
Now the thing about drug offenses, is the prosecutor must establish that the drug he claims you had, really was that drug. What that means is he's charging you with possession of 1 kg of cocaine, he must call an expert who personally tested a kilogram or more of the substance and concluded it was cocaine. The mentality is if you have 1 kg of baking soda and 1 g of cocaine, you can only be charged with possession of 1 g of cocaine, not 1 kg because not all of it is cocaine.
If the police interview the neighbors and judge them sufficiently reliable they could apply for a search warrant. Do they have probable cause to search your residence immediately? Maybe, addressed in next paragraph. Do they have the authority to search your residence? No, because they do not have a warrant. The only way they could justify the search is by arguing that they have an indication you would destroy the evidence of the crime. This indication is referred to as exigent circumstances.
However, let's say the neighbors just told the police they saw you smoking. Maybe it was weed. Probable cause may not exist for two reasons: 1.) smoking tobacco is legal and normal people do not have the sufficient training to distinguish the two, 2.) there is no evidence that searching your home would turn up more evidence, ie. there is no indication that you have more drugs in your home. Based on this, the police can continue their investigation and if they can corroborate the evidence given by the neighbors, they may be able to get a search warrant.
TL;DR: depends on what the neighbors tell the police. If sufficiently malicious they could get your house searched.
A "sufficiently malicious" neighbor could have your house and its contents seized, not just searched, and even if you're never charged with any crime, they can keep that property if they think they can either (a) convince people it's more likely than not that the property was involved in some kind of crime, a much lower standard than it takes for criminal convictions, or (b) bamboozle you with procedural requirements and expenses so you don't wind up getting a chance at (a). This is called Civil Asset Forefeiture and John Oliver's coverage of it can be found here.